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.
Using the two given points, we can first find the slope of the line:
slope = (change in y) / (change in x)
slope = (103-58) / (20-11)
slope = 45/9
slope = 5
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
58 = 5*11 + b
58 = 55 + b
b = 3
So the equation of the linear function is:
y = 5x + 3
(2,4) (-3,-1)
Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form.
Using the two given points, we can first find the slope of the line:
slope = (change in y) / (change in x)
slope = (-1-4) / (-3-2)
slope = (-5) / (-5)
slope = 1
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
4 = 1*2 + b
4 = 2 + b
b = 2
So 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.
We can use the two given points, (6, 120) and (8, 156), to find the slope of the line:
slope = (change in y) / (change in x)
slope = (156-120) / (8-6)
slope = 36/2
slope = 18
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
120 = 18*6 + b
120 = 108 + b
b = 12
So the equation of the linear function is:
y = 18x + 12