Parallel and perpendicular lines: compare slopes, and write the line through a point

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   The given line y = 2x − 8 has the step 2. Ren's line passes through (4, 1) and is perpendicular to y = 2x − 8. What is its rule in y = mx + b form?

   y = -x/2 + 3
2. 2.

   The given line y = -3x/2 + 1 has the step -3/2. Kira's line passes through (3, -2) and is perpendicular to y = -3x/2 + 1. What is its rule in y = mx + b form?

   y = 2x/3 − 4
3. 3.

   The given line y = x/3 − 2 has the step 1/3. Zee's line passes through (2, 5) and is perpendicular to y = x/3 − 2. What is its rule in y = mx + b form?

   y = -3x + 11

4. Read this first

   Input–output tables

   x	y
   AB 1	2
   3	8
   CD 0	5
   6	3

5. 4.

   Bo's line AB goes through (1, 2) and (3, 8). Line CD goes through (0, 5) and (6, 3). Are AB and CD parallel, perpendicular or neither?

   • Parallel
   • Neither, since the slopes are not equal
   • Perpendicular
6. 5.

   Pia's line AB goes through (0, 1) and (4, 3). Line CD goes through (2, 7) and (3, 5). Are AB and CD parallel, perpendicular or neither?

   • Neither
   • Perpendicular
   • Parallel
7. 6.

   The given line x = 4 is vertical. Luz's line passes through (2, 7) and is perpendicular to x = 4. What is the equation of the line?

   y = 7
8. 7.

   The given line y = -3 is horizontal. Ari's line passes through (5, 1) and is perpendicular to y = -3. What is the equation of the line?

   x = 5
9. 8.

   The given line x = -1 is vertical. Noah's line passes through (3, -6) and is perpendicular to x = -1. What is the equation of the line?

   y = -6
10. 9.

    The given line is 3x + 4y = 12. Ren's line passes through (4, 2) and is parallel to 3x + 4y = 12. What is its rule in y = mx + b form?

    y = -3x/4 + 5
11. 10.

    The given line is 5x − 2y = 10. Kira's line passes through (2, -3) and is parallel to 5x − 2y = 10. What is its rule in y = mx + b form?

    y = 5x/2 − 8