The equation of a function is y=−7x−12 . If this function were graphed, what would its slope be?(1 point
11 answers
The slope of a function is the coefficient of the x-term in its equation. In this case, the coefficient of x in the equation y = -7x - 12 is -7. Therefore, the slope of this function would be -7.
Use the table to answer the question.
x y
11 58
20 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
x y
11 58
20 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
To find the equation of the linear function that models the relationship between x and y in the table, we need to first find the slope (m) and the y-intercept (b).
Slope (m):
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now that we have the slope (m), we can use one of the points from the table (11, 58) to find the y-intercept (b).
Using the point (11, 58) in the equation y = mx + b:
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3
Slope (m):
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now that we have the slope (m), we can use one of the points from the table (11, 58) to find the y-intercept (b).
Using the point (11, 58) in the equation y = mx + b:
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3
Equations of Linear Functions Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 6 to 6 in one unit increments. The y-axis ranges from negative 4 to 6 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 3 comma negative 1 right parenthesis and left parenthesis 2 comma 4 right parenthesis.
Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form.
(1 point)
Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 6 to 6 in one unit increments. The y-axis ranges from negative 4 to 6 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 3 comma negative 1 right parenthesis and left parenthesis 2 comma 4 right parenthesis.
Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form.
(1 point)
To find the equation of the linear function represented by the graph passing through the points (-3, -1) and (2, 4), we first need to find the slope (m) using these two points.
slope (m) = (y₂ - y₁) / (x₂ - x₁)
slope (m) = (4 - (-1)) / (2 - (-3))
slope (m) = 5 / 5
slope (m) = 1
Now that we have the slope (m), we can use one of the points (let's take (-3, -1)) to find the y-intercept (b) in the form y = mx + b.
Using the point (-3, -1) in the equation y = mx + b:
-1 = 1(-3) + b
-1 = -3 + b
b = -1 + 3
b = 2
Therefore, the equation of the linear function shown on the graph is:
y = x + 2
slope (m) = (y₂ - y₁) / (x₂ - x₁)
slope (m) = (4 - (-1)) / (2 - (-3))
slope (m) = 5 / 5
slope (m) = 1
Now that we have the slope (m), we can use one of the points (let's take (-3, -1)) to find the y-intercept (b) in the form y = mx + b.
Using the point (-3, -1) in the equation y = mx + b:
-1 = 1(-3) + b
-1 = -3 + b
b = -1 + 3
b = 2
Therefore, the equation of the linear function shown on the graph is:
y = x + 2
Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y=mx+b form.(1 point)
To write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns, we can use the two given points: (6, 120) and (8, 156).
We first need to find the slope (m) using the points:
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (156 - 120) / (8 - 6)
Slope (m) = 36 / 2
Slope (m) = 18
Now that we have the slope, we can use one of the points (let's use (6, 120)) to find the y-intercept (b) in the form y = mx + b.
Using the point (6, 120) in the equation y = mx + b:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Therefore, the equation of the linear function that models the relationship is:
y = 18x + 12
We first need to find the slope (m) using the points:
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (156 - 120) / (8 - 6)
Slope (m) = 36 / 2
Slope (m) = 18
Now that we have the slope, we can use one of the points (let's use (6, 120)) to find the y-intercept (b) in the form y = mx + b.
Using the point (6, 120) in the equation y = mx + b:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Therefore, the equation of the linear function that models the relationship is:
y = 18x + 12
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 is a curve.
This is a nonlinear function. Its graph is a curve.
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 linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
This is a linear function. Its graph is a straight line with a slope of negative 4 and a y -intercept of 10.
This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.
Responses
This is a nonlinear function. Its graph is a curve.
This is a nonlinear function. Its graph is a curve.
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 linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
This is a linear function. Its graph is a straight line with a slope of negative 4 and a y -intercept of 10.
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 slope of -4 and a y-intercept of 10.
The slope of -4 indicates that for every 1 unit increase in x, the y-value decreases by 4 units. The intercept of 10 means that the graph crosses the y-axis at the point (0, 10). The graph of a linear function will be a straight line, and in this case, it will have a negative slope and pass through the point (0, 10).
The slope of -4 indicates that for every 1 unit increase in x, the y-value decreases by 4 units. The intercept of 10 means that the graph crosses the y-axis at the point (0, 10). The graph of a linear function will be a straight line, and in this case, it will have a negative slope and pass through the point (0, 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
−6
negative 6
−3
negative 3
6
6
2
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
−6
negative 6
−3
negative 3
6
6
2
The y-intercept of a function is the point where the graph crosses the y-axis. In the equation y = 2x - 6, the y-intercept occurs when x = 0, because the y-intercept occurs when x = 0.
When x = 0:
y = 2(0) - 6
y = -6
Therefore, the y-intercept of the function y = 2x - 6 is -6.
When x = 0:
y = 2(0) - 6
y = -6
Therefore, the y-intercept of the function y = 2x - 6 is -6.
1 answer