# Lesson 12

It’s All on the Line

- Let’s work with both parallel and perpendicular lines.

### Problem 1

For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?

- \(y=0.2x\)
- \(y=\text- 2x+1\)
- \(y=5x-3\)
- \((y-3)=\text- 5(x-4)\)
- \((y-1)=2(x-3)\)
- \(5x+y=3\)

### Problem 2

Main Street is parallel to Park Street. Park Street is parallel to Elm Street. Elm is perpendicular to Willow. How does Willow compare to Main?

### Problem 3

The line which is the graph of \(y=2x-4\) is transformed by the rule \((x,y)\rightarrow (\text-x,\text-y)\). What is the slope of the image?

### Problem 4

Select **all** equations whose graphs are lines perpendicular to the graph of \(3x+2y=6\).

\(3x-2y=4\)

\(2x+3y=6\)

\(2x-3y=8\)

\((y-4)=\frac23(x-6)\)

\((y-2)=\text-\frac{3}{2}(x-8)\)

\(y=\frac23x\)

\(y=\frac32x+3\)

### Problem 5

Match each line with a perpendicular line.

### Problem 6

The graph of \(y = \text{-} 4x + 2\) is translated by the directed line segment \(AB\) shown. What is the slope of the image?

### Problem 7

Select **all **points on the line with a slope of \(\text-\frac{1}2\) that go through the point \((4,\text-1)\).

\((\text-2, 2)\)

\((0,2)\)

\((4, \text-1)\)

\((0, 1)\)

\((\text-3, 8)\)

### Problem 8

One way to define a circle is that it is the set of all points that are the same distance from a given center. How does the equation \((x-h)^2+(y-k)^2=r^2\) relate to this definition? Draw a diagram if it helps you explain.