Equations of Linear Functions Quick Check
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Question
Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.(1 point)
Responses
This is a nonlinear function. Its graph has a maximum at (0,10).
This is a nonlinear function. Its graph has a maximum at left parenthesis 0 comma 10 right parenthesis .
This is a nonlinear function. Its graph is a curve.
This is a nonlinear function. Its graph is a curve.
This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.
This is a linear function. Its graph is a straight line with a y -intercept of negative 4 and a slope of 10.
This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
9 answers
This is a linear function. Its graph is a straight line with a slope of -4 and a y-intercept of 10.
Equations of Linear Functions Quick Check
2 of 52 of 5 Items
Question
The equation of a function is y=2x−6. If this function were graphed, what would its y-intercept be?(1 point)
Responses
2
2
−6
negative 6
6
6
−3
2 of 52 of 5 Items
Question
The equation of a function is y=2x−6. If this function were graphed, what would its y-intercept be?(1 point)
Responses
2
2
−6
negative 6
6
6
−3
The y-intercept of the function y=2x-6 would be -6.
Equations of Linear Functions Quick Check
3 of 53 of 5 Items
Question
Use the table to answer the question.
x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point)
Responses
y=10x−2
y equals 10 x minus 2
y=x+34
y equals x plus 34
y=10x+2
y equals 10 x plus 2
y=−10x+78
3 of 53 of 5 Items
Question
Use the table to answer the question.
x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
(1 point)
Responses
y=10x−2
y equals 10 x minus 2
y=x+34
y equals x plus 34
y=10x+2
y equals 10 x plus 2
y=−10x+78
To find the equation of a linear function, we need to determine the slope (m) and y-intercept (b).
We can calculate the slope using two points from the table:
m = (58 - 38) / (6 - 4) = 20 / 2 = 10.
Next, we can substitute one of the points into the equation y = mx + b to find the y-intercept:
38 = 10(4) + b
38 = 40 + b
b = -2
Therefore, the equation of the linear function is:
y = 10x - 2.
We can calculate the slope using two points from the table:
m = (58 - 38) / (6 - 4) = 20 / 2 = 10.
Next, we can substitute one of the points into the equation y = mx + b to find the y-intercept:
38 = 10(4) + b
38 = 40 + b
b = -2
Therefore, the equation of the linear function is:
y = 10x - 2.
Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.(1 point)
Responses
y=1,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3x+3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3x+1,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
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Responses
y=1,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 1,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3x+3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 3,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3x+1,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3 x plus 1,000 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
y=3,000x+3, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y equals 3,000 x plus 3 , where x is the number of months and y is the total amount of money Oliwia will have in her account.
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The correct equation of the linear function that models the relationship between the number of months and the total amount of money Oliwia will have in her account is:
y = 3x + 3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
y = 3x + 3,000, where x is the number of months and y is the total amount of money Oliwia will have in her account.
Question
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 3 to 3 in one unit increments. The y-axis ranges from negative 3 to 6 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 1 comma 0 right parenthesis.
Write the equation of the linear function shown on the graph.
(1 point)
Responses
y=2x−2
y equals 2 x minus 2
y=−2x−2
y equals negative 2 x minus 2
y=−2x+2
y equals negative 2 x plus 2
y=2x+2
y equals 2 x plus 2
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Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 3 to 3 in one unit increments. The y-axis ranges from negative 3 to 6 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 1 comma 4 right parenthesis and left parenthesis 1 comma 0 right parenthesis.
Write the equation of the linear function shown on the graph.
(1 point)
Responses
y=2x−2
y equals 2 x minus 2
y=−2x−2
y equals negative 2 x minus 2
y=−2x+2
y equals negative 2 x plus 2
y=2x+2
y equals 2 x plus 2
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To find the equation of the linear function given points (-1, 4) and (1, 0), we first need to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (-1, 4):
4 = -2(-1) + b
4 = 2 + b
b = 2
Therefore, the equation of the linear function is:
y = -2x + 2
So, the correct response is:
y = -2x + 2
m = (y2 - y1) / (x2 - x1)
m = (0 - 4) / (1 - (-1))
m = -4 / 2
m = -2
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (-1, 4):
4 = -2(-1) + b
4 = 2 + b
b = 2
Therefore, the equation of the linear function is:
y = -2x + 2
So, the correct response is:
y = -2x + 2
1 answer