What method can be used to write the equation of a line in slope-intercept form given two points?
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope.
32 answers
Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.
Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116
Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116
Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116
Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116
Using the two given points (4, 74) and (6, 86), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (86 - 74) / (6 - 4)
m = 12 / 2
m = 6
Now we have the slope and can use one of the points to find the y-intercept:
y = mx + b
74 = 6(4) + b
74 = 24 + b
b = 50
Therefore, the linear equation that represents Catherine's situation is:
y = 6x + 50
m = (y2 - y1) / (x2 - x1)
m = (86 - 74) / (6 - 4)
m = 12 / 2
m = 6
Now we have the slope and can use one of the points to find the y-intercept:
y = mx + b
74 = 6(4) + b
74 = 24 + b
b = 50
Therefore, the linear equation that represents Catherine's situation is:
y = 6x + 50
Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2. This is the slope of the line passing through the two points.
Miguel volunteers at his local food pantry and takes note of how much money is donated each day during a 10-day fundraising phone-a-thon. Below is the graph that represents the data that he collected.
A graph titled Food Pantry Donations has number of days on the x-axis and dollars donated on the y-axis. A line goes through points (1, 75) and (2, 100).
The slope of the line that represents the data that Miguel collected is 25, and the y-intercept is 50. What do the slope and y-intercept represent in Miguel’s situation?
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
A graph titled Food Pantry Donations has number of days on the x-axis and dollars donated on the y-axis. A line goes through points (1, 75) and (2, 100).
The slope of the line that represents the data that Miguel collected is 25, and the y-intercept is 50. What do the slope and y-intercept represent in Miguel’s situation?
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
The slope indicates that the food pantry collects $50 each day. The y-intercept indicates that the pantry began with $25 in its donation account.
The slope indicates that the food pantry collects $25 each day. The y-intercept indicates that the pantry began with $50 in its donation account.
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
Step 1: m = StartFraction 13 minus 25 Over negative 4 minus (negative 7) EndFraction = StartFraction negative 12 Over 3 EndFraction = negative 4. Step 2: y = negative 4 x + b. 25 = negative 4 (negative 7) + b. 25 = 28 + b. 25 minus 28 = 28 + b minus 28. b = negative 3. Step 3: y = negative 3 x minus 4
What was Brooke’s error?
She found the incorrect slope in step 1.
She mixed up the x- and y-coordinates when she plugged in the point in step 2.
She found the incorrect y-intercept in step 2.
She mixed up the slope and y-intercept when she wrote the equation in step 3.
She found the incorrect y-intercept in step 2.
The correct calculation in step 2 should be:
25 = -4(-7) + b
25 = 28 + b
b = -3
So the equation should be:
y = -4x - 3
The correct calculation in step 2 should be:
25 = -4(-7) + b
25 = 28 + b
b = -3
So the equation should be:
y = -4x - 3
Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the graph, then it must be the same function.
On a coordinate plane, a line goes through points (0, negative 1) and (2, 0).
Which equation proves Jeremy’s argument is incorrect?
y = negative one-half x minus 1
y = negative one-half x + 1
y = one-half x minus 1
y = one-half x + 1
On a coordinate plane, a line goes through points (0, negative 1) and (2, 0).
Which equation proves Jeremy’s argument is incorrect?
y = negative one-half x minus 1
y = negative one-half x + 1
y = one-half x minus 1
y = one-half x + 1
y = negative one-half x + 1 proves Jeremy’s argument is incorrect.
This is because the equation has the same slope as the given line (-1/2) but a different y-intercept (1 instead of -1). Therefore, it represents a different line with the same slope but a different y-intercept.
This is because the equation has the same slope as the given line (-1/2) but a different y-intercept (1 instead of -1). Therefore, it represents a different line with the same slope but a different y-intercept.
Lindsay used two points, (x 1, y 1) and (x 2, y 2), to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. Given this information, which expression must represent the value of b?
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y1 – ( (y2 – y1) / (x2 – x1) ) (x1) must represent the value of b.
Lindsay used two points, (x 1, y 1) and (x 2, y 2), to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. Given this information, which expression must represent the value of b?
A)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
B)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
C)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
D)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
A)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
B)y 1 minus (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
C)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 1)
D)y 1 + (StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction) (x 2)
y1 – ( (y2 – y1) / (x2 – x1) ) (x1) must represent the value of b.
The price of a particular stock is represented by the linear equation y = negative 0.91 x + 103.47, where x represents the number of weeks the stock has been owned and y represents the price of the stock, in dollars. If this relationship continues, what is the price of the stock after it has been owned for 12 weeks?
$92.55
$94.37
$100.52
$114.39
$92.55
$94.37
$100.52
$114.39
The price of the stock after it has been owned for 12 weeks is:
y = -0.91x + 103.47 (where x = 12)
y = -0.91(12) + 103.47
y = -10.92 + 103.47
y = 92.55
Therefore, the price of the stock after it has been owned for 12 weeks is $92.55.
Answer: $92.55
y = -0.91x + 103.47 (where x = 12)
y = -0.91(12) + 103.47
y = -10.92 + 103.47
y = 92.55
Therefore, the price of the stock after it has been owned for 12 weeks is $92.55.
Answer: $92.55
The value of a collectible coin can be represented by the equation y = 2 x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it?
$4.87
$7.74
$9.74
$19.48
$4.87
$7.74
$9.74
$19.48
The value of the coin when Consuello originally purchased it can be found by setting x = 0:
y = 2x + 9.74 (where x = 0)
y = 2(0) + 9.74
y = 9.74
Therefore, the value of the coin when Consuello originally purchased it was $9.74.
Answer: $9.74
y = 2x + 9.74 (where x = 0)
y = 2(0) + 9.74
y = 9.74
Therefore, the value of the coin when Consuello originally purchased it was $9.74.
Answer: $9.74
Vladimir says that the equation of the line that passes through points (negative 5, negative 3) and (10, 9) is y = four-fifths x + 1. Robyn says that the line passes through the points (negative 10, negative 7) and (negative 15, negative 11). Who is correct?
only Vladimir
only Robyn
both Vladimir and Robyn
neither Vladimir nor Robyn
only Vladimir
only Robyn
both Vladimir and Robyn
neither Vladimir nor Robyn
Only Vladimir is correct.
We can confirm this by using the slope-intercept form:
m = (y2 - y1) / (x2 - x1)
m = (9 - (-3)) / (10 - (-5))
m = 12 / 15
m = 4/5
Now we have the slope m and can use one of the points to find the y-intercept:
y = mx + b
-3 = (4/5)(-5) + b
-3 = -4 + b
b = 1
Therefore, the equation of the line is:
y = (4/5)x + 1
On the other hand, the points (-10, -7) and (-15, -11) have a slope:
m = (-11 - (-7)) / (-15 - (-10))
m = -4 / -5
m = 4/5
However, using the first point:
-7 = (4/5)(-10) + b
-7 = -8 + b
b = 1
Therefore, the equation of the line passing through the points (-10, -7) and (-15, -11) is:
y = (4/5)x + 1
Since Vladimir's equation and Robyn's equation are the same, only Vladimir is correct.
We can confirm this by using the slope-intercept form:
m = (y2 - y1) / (x2 - x1)
m = (9 - (-3)) / (10 - (-5))
m = 12 / 15
m = 4/5
Now we have the slope m and can use one of the points to find the y-intercept:
y = mx + b
-3 = (4/5)(-5) + b
-3 = -4 + b
b = 1
Therefore, the equation of the line is:
y = (4/5)x + 1
On the other hand, the points (-10, -7) and (-15, -11) have a slope:
m = (-11 - (-7)) / (-15 - (-10))
m = -4 / -5
m = 4/5
However, using the first point:
-7 = (4/5)(-10) + b
-7 = -8 + b
b = 1
Therefore, the equation of the line passing through the points (-10, -7) and (-15, -11) is:
y = (4/5)x + 1
Since Vladimir's equation and Robyn's equation are the same, only Vladimir is correct.
Which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?
The slope is One-half.
The slope is Negative 2.
The y-intercept is 7.
The y-intercept is 13.
The slope is One-half.
The slope is Negative 2.
The y-intercept is 7.
The y-intercept is 13.
The characteristic of the line that passes through the points (6, 10) and (12, 7) is that the slope is negative 2.
Using the formula for slope:
m = (y2 - y1) / (x2 - x1)
m = (7 - 10) / (12 - 6)
m = -3 / 6
m = -1/2
However, this is not one of the answer choices. The correct slope can be found by simplifying the fraction:
m = -3 / 6
m = -1 / 2
Therefore, the slope is negative 2, and none of the answer choices are correct.
Using the formula for slope:
m = (y2 - y1) / (x2 - x1)
m = (7 - 10) / (12 - 6)
m = -3 / 6
m = -1/2
However, this is not one of the answer choices. The correct slope can be found by simplifying the fraction:
m = -3 / 6
m = -1 / 2
Therefore, the slope is negative 2, and none of the answer choices are correct.
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45 x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
Mark this and return
the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
Mark this and return
The slope represents the cost for each hour it takes to repair the machine.
What is the equation in slope-intercept form of the linear function represented by the table?
x
y
–6
–18
–1
–8
4
2
9
12
y = negative 2 x minus 6
y = negative 2 x + 6
y = 2 x minus 6
y = 2 x + 6
x
y
–6
–18
–1
–8
4
2
9
12
y = negative 2 x minus 6
y = negative 2 x + 6
y = 2 x minus 6
y = 2 x + 6
The equation in slope-intercept form of the linear function represented by the table is y = -2x + 6.
Using the points (-6, -18) and (-1, -8), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-8 - (-18)) / (-1 - (-6))
m = 10 / 5
m = 2
Now we have the slope, and we can use one of the points to find the y-intercept:
y = mx + b
-8 = 2(-1) + b
-8 = -2 + b
b = 6
Therefore, the equation in slope-intercept form is:
y = -2x + 6
Using the points (-6, -18) and (-1, -8), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-8 - (-18)) / (-1 - (-6))
m = 10 / 5
m = 2
Now we have the slope, and we can use one of the points to find the y-intercept:
y = mx + b
-8 = 2(-1) + b
-8 = -2 + b
b = 6
Therefore, the equation in slope-intercept form is:
y = -2x + 6
Bob and Carl each rented the same kind of moving truck from EZ Move. There was a flat rental fee plus a charge per mile that the truck was driven. Bob’s cost for his truck was $112.96 for 138 miles. Carl’s cost for his truck was $142.78 for 209 miles. Which equation can be used to represent the cost of the rental truck?
Round to the nearest hundredth if necessary.
y = 71 x minus 29.82
y = 25 x minus 66
y = 0.42 x + 71
y = 0.42 x + 55
Round to the nearest hundredth if necessary.
y = 71 x minus 29.82
y = 25 x minus 66
y = 0.42 x + 71
y = 0.42 x + 55
We can start by using the point-slope form of a linear equation:
y - y1 = m(x - x1)
Let (x1, y1) be the point (138, 112.96) for Bob's cost and (209, 142.78) for Carl's cost. We can then find the slope m:
m = (y2 - y1) / (x2 - x1)
m = (142.78 - 112.96) / (209 - 138)
m = 29.82 / 71
m = 0.42
Now we have the slope, and we can use one of the points to find the y-intercept:
y - y1 = m(x - x1)
y - 112.96 = 0.42(x - 138)
y - 112.96 = 0.42x - 57.96
y = 0.42x + 55
Therefore, the equation that represents the cost of the rental truck is:
y = 0.42x + 55
Answer: y = 0.42 x + 55
y - y1 = m(x - x1)
Let (x1, y1) be the point (138, 112.96) for Bob's cost and (209, 142.78) for Carl's cost. We can then find the slope m:
m = (y2 - y1) / (x2 - x1)
m = (142.78 - 112.96) / (209 - 138)
m = 29.82 / 71
m = 0.42
Now we have the slope, and we can use one of the points to find the y-intercept:
y - y1 = m(x - x1)
y - 112.96 = 0.42(x - 138)
y - 112.96 = 0.42x - 57.96
y = 0.42x + 55
Therefore, the equation that represents the cost of the rental truck is:
y = 0.42x + 55
Answer: y = 0.42 x + 55
Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).
x
y
1
7
2
5
3
3
4
1
What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18
x
y
1
7
2
5
3
3
4
1
What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18
Using the points (2, 5) and (4, 1), we can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (1 - 5) / (4 - 2)
m = -4/2
m = -2
Now we have the slope, and we can use one of the points to find the y-intercept:
y = mx + b
1 = -2(4) + b
1 = -8 + b
b = 9
Therefore, the equation in slope-intercept form is:
y = -2x + 9
So Misty would have gotten the same equation (y = -2x +
m = (y2 - y1) / (x2 - x1)
m = (1 - 5) / (4 - 2)
m = -4/2
m = -2
Now we have the slope, and we can use one of the points to find the y-intercept:
y = mx + b
1 = -2(4) + b
1 = -8 + b
b = 9
Therefore, the equation in slope-intercept form is:
y = -2x + 9
So Misty would have gotten the same equation (y = -2x +
What is the equation of the line that passes through the points (15, 9) and (-2, 9)?
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1 answer