Model the data in the table with a linear equation in slope-intercept form. Then tell what the slope and y-intercept represent.
time work wages earned y ($)
x (h)
1 10.00
3 30.00
6 60.00
9 90.00
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 assess the relationship between the time worked (x) and the wages earned (y).
Looking at the table, we can observe that the wages earned (y) are directly proportional to the time worked (x). In other words, for every increase in x, y also increases by a constant amount.
We can determine the slope (m) by calculating the change in y divided by the change in x. Taking any two data points from the table, we have:
Slope (m) = (Change in y)/(Change in x) = (y2 - y1)/(x2 - x1)
Let's calculate the slope using the first and last data points:
Slope (m) = (90 - 10)/(9 - 1) = 80/8 = 10
To find the y-intercept (b), we can substitute any known data point into the slope-intercept form equation (y = mx + b) and solve for b.
Using the first data point (x = 1, y = 10):
10 = 10(1) + b
10 = 10 + b
b = 10 - 10
b = 0
Therefore, the linear equation in slope-intercept form is:
y = 10x + 0
y = 10x
The slope (10) represents the constant rate at which wages are earned per hour, indicating that for every hour worked, $10 is earned.
The y-intercept (0) represents the initial value of y, which is 0. In this case, it means that if no time is worked, no wages are earned.
What does the y-intercept represent?
A.
The initial wages earned in dollars
B.
The final wages earned in dollars
C.
The final time worked in dollars
D.
The initial time worked in hours