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, x (h): 1,3,6,9
wages earned, y ($): 8.50, 25.50, 51.00, 76.50
To model the data in the table with a linear equation in slope-intercept form, we can use the formula y = mx + b, where y represents the wages earned, x represents the time worked, m is the slope, and b is the y-intercept.
Using the given data points, we can find the slope (m) and y-intercept (b) by selecting any two data points and calculating the rise (change in y) over run (change in x).
Using the points (1, 8.50) and (3, 25.50):
m = (25.50 - 8.50) / (3 - 1) = 17 / 2 = 8.50
Now, let's use the slope and one of the data points (1, 8.50) to find the y-intercept (b):
8.50 = 8.50(1) + b
8.50 = 8.50 + b
b = 8.50 - 8.50
b = 0
Therefore, the equation that models the data in the table in slope-intercept form is: y = 8.50x + 0.
The slope (8.50) represents the rate at which wages increase for each hour worked. It means that for every additional hour worked, the wages increase by $8.50.
The y-intercept (0) represents the starting point, or the initial wages earned when no hours are worked. In this case, it indicates that when no hours are worked, no wages are earned.