The graph of a function is a straight line with a slope of 2 and a y-intercept of 7. What is the equation of the function? Write your answer in y = mx + b form.
y = 2x + 7
The equation of a function is y = −7x − 12. If this function were graphed, what would its slope be?
The slope of the function y = -7x - 12 is -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.
First, we need to find the slope (m) of the linear function using the two points (11, 58) and (20, 103).
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now that we have the slope, we can choose one point and the slope to find the y-intercept (b).
Using point (20, 103):
103 = 5(20) + b
103 = 100 + b
b = 103 - 100
b = 3
Therefore, the equation of the linear function is:
y = 5x + 3
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.
First, we need to find the slope (m) of the linear function using the two points (-3, -1) and (2, 4).
m = (y2 - y1) / (x2 - x1)
m = (4 - (-1)) / (2 - (-3))
m = (4 + 1) / (2 + 3)
m = 5 / 5
m = 1
Now, we can choose one point and the slope to find the y-intercept (b). Using point (-3, -1):
-1 = 1(-3) + b
-1 = -3 + b
b = -1 + 3
b = 2
Therefore, the equation of the linear function 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.
Let y represent the amount of money Esperanza earns and x represent the number of hours she works. We have two points: (6, 120) and (8, 156).
First, find the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1)
m = (156 - 120) / (8 - 6)
m = 36 / 2
m = 18
Now, we can choose one point and the slope to find the y-intercept (b). Using point (6, 120):
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Therefore, the equation of the linear function is:
y = 18x + 12
Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.
A. This is a linear function. Its graph is a straight line with a y-intercept of −4 and a slope of 10.
B. This is a nonlinear function. Its graph is a curve.
C. This is a linear function. Its graph is a straight line with a slope of −4 and a y-intercept of 10.
D. This is a nonlinear function. Its graph has a maximum at (0,10).