Part 1 of 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 6.00 18.00 369 36.00 54.00
Write the linear equation in slope-intercept form.
y = __
(integers or decimals for any numbers in the expression.)
To find the linear equation in slope-intercept form, we need to first find the slope (m) and the y-intercept (b).
We can use the formula for finding the slope of a line given two points (x1, y1) and (x2, y2):
m = (y2 - y1) / (x2 - x1)
Let's choose the points (1, 6.00) and (18.00, 36.00) from the table:
m = (36.00 - 6.00) / (18.00 - 1) = 30 / 17 ≈ 1.7647
Now, we can use the slope-intercept form of a linear equation:
y = mx + b
Substituting the values of m and one of the points (let's use (1, 6.00)):
6.00 = 1.7647 * 1 + b
6.00 = 1.7647 + b
b ≈ 6 - 1.7647 ≈ 4.2353
The linear equation in slope-intercept form is:
y = 1.7647x + 4.2353
Now, let's discuss what the slope and y-intercept represent:
The slope (1.7647) represents the rate at which the wages earned (y) increase with each additional hour worked (x). In this case, for every hour worked, the wages increase by approximately $1.7647.
The y-intercept (4.2353) represents the initial amount of wages earned (y) when no hours are worked (x = 0). In this case, when no hours are worked, the individual still earns approximately $4.2353.