Model the data in the table with a linear equation in​ slope-intercept form. Then tell what the slope and​ y-intercept represent.

Question

Time​ Worked, x​ (h) 1 3 6 9
Wages​ Earned, y​ ($) 9.00 27.00 54.00 81.00

Write the linear equation in​ slope-intercept form.
y=

​(Use integers or decimals for any numbers in the​ expression.)

Answer 1

To find the linear equation in slope-intercept form, we need to find the slope and y-intercept.

First, let's calculate the slope (m):
m = (change in y) / (change in x)
Using the points (1, 9) and (3, 27):
m = (27 - 9) / (3 - 1) = 18 / 2 = 9

Next, let's find the y-intercept (b):
Using the point (1, 9) and substituting the slope (m = 9):
9 = 9(1) + b
9 = 9 + b
b = 0

So the linear equation in slope-intercept form is:
y = 9x

The slope represents the rate at which wages are earned per hour worked. In this case, the slope of 9 means that for every hour worked, the wage earned increases by $9.
The y-intercept represents the starting point or the initial amount earned without any hours worked. In this case, since the y-intercept is 0, it means that if no hours are worked, no wages are earned.