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?

graph on line L, y intercept of 1 and slope of 1 over 5
  1. \(y=0.2x\)
  2. \(y=\text- 2x+1\)
  3. \(y=5x-3\)
  4. \((y-3)=\text- 5(x-4)\)
  5. \((y-1)=2(x-3)\)
  6. \(5x+y=3\)

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 \(3x+2y=6\).















(From Unit 6, Lesson 11.)

Problem 5

Match each line with a perpendicular line. 

(From Unit 6, Lesson 11.)

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?

graph of y = -4x + 2
(From Unit 6, Lesson 10.)

Problem 7

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


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




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


\((0, 1)\)


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

(From Unit 6, Lesson 9.)

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.

(From Unit 6, Lesson 4.)