Question
Complete the slope-intercept form of an equation that represents the relationship in the table.
Answers
Answer
Complete the slope-intercept form of an equation that represents the relationship in the table.
x | y
-3 | 3(1/2)
7 | -1(1/2)
9 | -2(1/2)
x | y
-3 | 3(1/2)
7 | -1(1/2)
9 | -2(1/2)
Answer
not correct
Answer
still not correct
Answer
Complete the slope-intercept form of an equation that represents the relationship in the table.
x | y
0 | 2
1 | 0
x | y
0 | 2
1 | 0
Answer
Complete the slope-intercept form of an equation that represents the relationship in the table.
x | y
2 | 1
4 | -3
x | y
2 | 1
4 | -3
Answered by
GPT 3.5
To complete the slope-intercept form of an equation, we need to find the slope (m) and the y-intercept (b) using the given table of values.
Let's assume the following data to be represented in the table:
x | y
1 | 2
2 | 4
3 | 6
To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1) = (4 - 2) / (2 - 1) = 2 / 1 = 2
Now that we have the slope (m), we can use the formula for the slope-intercept form of an equation:
y = mx + b
Next, let's choose one of the points to substitute the values of x and y into the equation to find the y-intercept (b). Let's use the point (1,2):
2 = 2(1) + b
2 = 2 + b
b = 2 - 2
b = 0
So, the completed slope-intercept form of the equation is:
y = 2x + 0
y = 2x
Let's assume the following data to be represented in the table:
x | y
1 | 2
2 | 4
3 | 6
To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1) = (4 - 2) / (2 - 1) = 2 / 1 = 2
Now that we have the slope (m), we can use the formula for the slope-intercept form of an equation:
y = mx + b
Next, let's choose one of the points to substitute the values of x and y into the equation to find the y-intercept (b). Let's use the point (1,2):
2 = 2(1) + b
2 = 2 + b
b = 2 - 2
b = 0
So, the completed slope-intercept form of the equation is:
y = 2x + 0
y = 2x
Answered by
GPT 3.5
To find the equation of the line that represents the relationship in the table using the slope-intercept form (y = mx + b), we first need to calculate the slope (m). The slope can be found using two points from the table.
Let's use the points (-3, 3/2) and (9, -2 1/2) to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = ((-2 1/2) - 3/2) / (9 - (-3))
m = (-5/2 - 3/2) / 12
m = (-8/2) / 12
m = -4 / 12
m = -1/3
Now that we have the slope, m = -1/3, we need to find the y-intercept, b. We can do this by substituting the slope and one of the points into the slope-intercept form:
Using the point (-3, 3/2):
3/2 = -1/3 * (-3) + b
3/2 = 1 + b
b = 3/2 - 1
b = 1/2
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -1/3x + 1/2
Let's use the points (-3, 3/2) and (9, -2 1/2) to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = ((-2 1/2) - 3/2) / (9 - (-3))
m = (-5/2 - 3/2) / 12
m = (-8/2) / 12
m = -4 / 12
m = -1/3
Now that we have the slope, m = -1/3, we need to find the y-intercept, b. We can do this by substituting the slope and one of the points into the slope-intercept form:
Using the point (-3, 3/2):
3/2 = -1/3 * (-3) + b
3/2 = 1 + b
b = 3/2 - 1
b = 1/2
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -1/3x + 1/2
Answered by
GPT 3.5
Let's correct the calculation. We'll use the points (7, -1 1/2) and (-3, 3 1/2) to determine the slope:
m = (y2 - y1) / (x2 - x1)
m = (-1 1/2 - 3 1/2) / (7 - (-3))
m = (-3 - 7) / (7 + 3)
m = (-4) / (10)
m = -4/10
m = -2/5
Now, we substitute one of the points (let's use (7, -1 1/2)) and the slope into the slope-intercept form equation to find the y-intercept (b):
-1 1/2 = (-2/5)(7) + b
-1 1/2 = -14/5 + b
b = -1 1/2 + 14/5
b = -3/2 + 14/5
b = -15/10 + 28/10
b = 13/10
Therefore, the completed slope-intercept form of the equation is:
y = -2/5x + 13/10
m = (y2 - y1) / (x2 - x1)
m = (-1 1/2 - 3 1/2) / (7 - (-3))
m = (-3 - 7) / (7 + 3)
m = (-4) / (10)
m = -4/10
m = -2/5
Now, we substitute one of the points (let's use (7, -1 1/2)) and the slope into the slope-intercept form equation to find the y-intercept (b):
-1 1/2 = (-2/5)(7) + b
-1 1/2 = -14/5 + b
b = -1 1/2 + 14/5
b = -3/2 + 14/5
b = -15/10 + 28/10
b = 13/10
Therefore, the completed slope-intercept form of the equation is:
y = -2/5x + 13/10
Answered by
GPT 3.5
Let's use the points to find the correct slope and y-intercept.
Given points:
(-3, 3 1/2) = 7/2
(7, -1 1/2) = -3/2
First, let's calculate the slope using the two points:
m = (y2 - y1) / (x2 - x1)
m = ((-3/2) - (7/2)) / (7 - (-3))
m = (-3/2 - 7/2) / (7 + 3)
m = (-10/2) / 10
m = -5/10
m = -1/2
Now, let's substitute the slope into the slope-intercept form equation and use one of the points to find the y-intercept:
Using point (-3, 7/2):
7/2 = -1/2 * (-3) + b
7/2 = 3/2 + b
b = 7/2 - 3/2
b = 4/2
b = 2
Therefore, the completed slope-intercept form of the equation is:
y = -1/2x + 2
Given points:
(-3, 3 1/2) = 7/2
(7, -1 1/2) = -3/2
First, let's calculate the slope using the two points:
m = (y2 - y1) / (x2 - x1)
m = ((-3/2) - (7/2)) / (7 - (-3))
m = (-3/2 - 7/2) / (7 + 3)
m = (-10/2) / 10
m = -5/10
m = -1/2
Now, let's substitute the slope into the slope-intercept form equation and use one of the points to find the y-intercept:
Using point (-3, 7/2):
7/2 = -1/2 * (-3) + b
7/2 = 3/2 + b
b = 7/2 - 3/2
b = 4/2
b = 2
Therefore, the completed slope-intercept form of the equation is:
y = -1/2x + 2
Answered by
GPT 3.5
To find the equation of the line that represents the relationship in the table using the slope-intercept form (y = mx + b), we first need to calculate the slope (m). The slope can be found using the two points (0, 2) and (1, 0) from the table.
Let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - 2) / (1 - 0)
m = -2 / 1
m = -2
Now that we have the slope, m = -2, we can find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form:
Using the point (0, 2):
2 = -2(0) + b
b = 2
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -2x + 2
Let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - 2) / (1 - 0)
m = -2 / 1
m = -2
Now that we have the slope, m = -2, we can find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form:
Using the point (0, 2):
2 = -2(0) + b
b = 2
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -2x + 2
Answered by
GPT 3.5
To find the equation of the line that represents the relationship in the table using the slope-intercept form (y = mx + b), we first need to calculate the slope (m). The slope can be found using the two points (2, 1) and (4, -3) from the table.
Let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-3 - 1) / (4 - 2)
m = -4 / 2
m = -2
Now that we have the slope, m = -2, we can find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form:
Using the point (2, 1):
1 = -2(2) + b
1 = -4 + b
b = 1 + 4
b = 5
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -2x + 5
Let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-3 - 1) / (4 - 2)
m = -4 / 2
m = -2
Now that we have the slope, m = -2, we can find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form:
Using the point (2, 1):
1 = -2(2) + b
1 = -4 + b
b = 1 + 4
b = 5
Now that we have determined the slope and y-intercept, the equation of the line in slope-intercept form is:
y = -2x + 5
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