Question

The table shows the total amounts of y (in thousands of dollars) of money a homeowner saves on electric bills x years after installing solar panels.

A. Write an equation that models the total amount of money saved as a function of the number of years after the solar panels were installed. (Use the points (0, -12) and (15, 10.5) to write the equation).

B. Interpret the slope and y-intercept of the line of fit.​

Answer 1

The linear equation that models this is:

y = 1.5*x - 12

• The y-intercept means that at x = 0 (the initial year) he owes 12 thousand dollars.
• the slope of 1.5 means that each year, he saves 1.5 thousand dollars

How to write the linear equation:

A general linear equation in slope-intercept form is written as:

y = a*x + b

Where a is the slope and b is the y-intercept

Here we can use the point (0, -12) to know that the y-intercept is -12, then we can write:

y = a*x - 12

We also have the point (15, 10.5), replacing these values we will get:

10.5 = a*15 - 12

10.5 + 12 = a*15

22.5 = a*15

22.5/15 = a

1.5 = a

The linear equation is:

y = 1.5*x - 12

B) The y-intercept means that at x = 0 (the initial year) he owes 12 thousand dollars.

the slope of 1.5 means that each year, he saves 1.5 thousand dollars