Model the data in the table with a linear equation in slope-intercept form. Then tell what the slope and y-intercept represent.
Time Worked, Wages Earned, x (h) y ($) 1 8.00 24.00 369 48.00 72.00
Write the linear equation in slope-intercept form.
y =___
(Use integers or decimals for any numbers in the expression.)
To find the linear equation in slope-intercept form, we need to find the slope (m) and y-intercept (b) using the given data points.
First, let's find the slope:
m = (change in y)/(change in x)
For the points (1, 8.00) and (3, 24.00):
m = (24.00 - 8.00)/(3 - 1)
m = 16.00/2
m = 8.00
Now, let's find the y-intercept using the slope and one of the given points, (1, 8.00):
y = mx + b
8.00 = 8.00(1) + b
8.00 = 8.00 + b
b = 0
Therefore, the slope-intercept form of the linear equation is:
y = 8x + 0
However, since the y-intercept is 0, we can simplify the equation to:
y = 8x
The slope (8) represents the rate at which wages are earned per hour worked. In this case, for every hour worked, $8.00 is earned.
The y-intercept (0) represents the starting point of the earnings, indicating that no wages are earned without any hours worked.