Yesterday, Ezera worked for 6 hours and earned $120. Today, he worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Ezera works and the amount of money she earns. Enter your answer in y = mx + b form.
We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (6, 120) and (x2, y2) = (8, 156)
m = (156 - 120) / (8 - 6) = 18
So the slope is 18.
To find the y-intercept, we can use one of the points and the slope. Let's use the point (6, 120).
y = mx + b
120 = 18(6) + b
120 = 108 + b
b = 12
So the y-intercept is 12.
Putting it all together, the equation of the linear function that models the relationship between the number of hours Ezera works and the amount of money she earns is:
y = 18x + 12
To write the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
The slope (m) can be calculated by finding the change in y divided by the change in x. In this case, y represents the amount of money earned and x represents the number of hours worked.
Change in y = $156 - $120 = $36
Change in x = 8 hours - 6 hours = 2 hours
So, the slope (m) = Change in y / Change in x = $36 / 2 hours = $18/hour.
To find the y-intercept (b), we can substitute one set of values into the equation y = mx + b. Using the first set of data, 6 hours of work and $120 earned:
120 = 18(6) + b
120 = 108 + b
b = 120 - 108
b = 12
Therefore, the equation of the linear function that models the relationship between the number of hours Ezera works (x) and the amount of money she earns (y) is:
y = 18x + 12