# Lesson 7

Translating to $y=mx+b$

Let’s see what happens to the equations of translated lines.

### Problem 1

Select **all** the equations that have graphs with the same \(y\)-intercept.

A:

\(y=3x -8\)

B:

\(y=3x -9\)

C:

\(y=3x+8\)

D:

\(y=5x -8\)

E:

\(y=2x -8\)

F:

\(y=\frac13x -8\)

### Problem 2

Create a graph showing the equations \(y=\frac14x\) and \(y=\frac14x-5\). Explain how the graphs are the same and how they are different.

### Problem 3

A cable company charges $70 per month for cable service to existing customers.

- Find a linear equation representing the relationship between \(x\), the number of months of service, and \(y\), the total amount paid in dollars by an existing customer.
- For new customers, there is an additional one-time $100 service fee. Repeat the previous problem for new customers.
- When the two equations are graphed in the coordinate plane, how are they related to each other geometrically?

### Problem 4

A mountain road is 5 miles long and gains elevation at a constant rate. After 2 miles, the elevation is 5500 feet above sea level. After 4 miles, the elevation is 6200 feet above sea level.

- Find the elevation of the road at the point where the road begins.
- Describe where you would see the point in part (a) on a graph where \(y\) represents the elevation in feet and \(x\) represents the distance along the road in miles.

### Problem 5

Match each graph to a situation.