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.
