Multiple Representations The Coughline family is driving from Boston to Chicago. The total distance of the trip is 986 miles and each hour they will drive 65 miles.

a. Algebra Write an equation to represent the number of remaining miles y after driving any number of hours x.

b. Graphs Graph the equation from part a on a coordinate plane.

c. Numbers What is the rate of change and y-intercept of the line?

d. Words Explain why the line slopes down by 65 for each hour.

e. Words Why does the line cross the y-axis at 986?

Persevere with Problems Explain why a horizontal line has a rate of change of zero.

Model with Mathematics Write and solve a real-world problem in which you need to find the initial value of a function. Then explain to a classmate how you solved your problem.

Justify Conclusions Your teacher asks you to write a linear equation for a function in which the rate of change is -7 and the initial value is -2. You wrote the equation \(\text{y} = -7\text{x} + (-2)\). Your classmate wrote the equation \(\text{y} = -7\text{x} - 2\). Another classmate wrote the equation \(\text{y} = (-2) + (-7)\text{x}\). Your teacher wrote the equation \(\text{y} = -2 - 7\text{x}\). Who is correct? Justify your response.