Lesson 3: Writing Equations of Parallel and Perpendicular Lines — Practice Questions

1. 1. Are the lines $y = -4x + 7$ and $y = -4x - 1$ parallel, perpendicular, or neither?

   • A. Parallel
   • B. Perpendicular
   • C. Neither

2. 2. Are the lines $2x - 5y = 10$ and $4x - 10y = 30$ parallel, perpendicular, or neither?

   • A. Parallel
   • B. Perpendicular
   • C. Neither

3. 3. The line $y = 7x - 4$ has slope $m = 7$. A line parallel to it must have a slope of ___.

4. 4. Which line is parallel to $y = 2x + 9$?

   • A. $y = 2x - 5$
   • B. $y = -2x + 9$
   • C. $y = \frac{1}{2}x + 9$
   • D. $y = 3x + 9$

5. 5. Are the lines $3x + y = 8$ and $6x + 2y = 5$ parallel, perpendicular, or neither?

   • A. Parallel
   • B. Perpendicular
   • C. Neither

6. 6. Write the equation in point-slope form for a line parallel to $y = 3x - 1$ that passes through the point $(4, 7)$. Equation: ___

7. 7. Which equation represents a line perpendicular to $y = -4x + 9$ and passing through the point $(8, 1)$?

   • A. y - 1 = -4(x - 8)
   • B. $y - 1 = \frac{1}{4}(x - 8)$
   • C. $y - 8 = \frac{1}{4}(x - 1)$
   • D. $y - 1 = -\frac{1}{4}(x - 8)$

8. 8. A line passes through $(-3, 6)$ and is parallel to the line $5x - 2y = 10$. Write its equation in point-slope form. Equation: ___

9. 9. Which equation represents the line passing through $(4, -2)$ and perpendicular to the line $2x + 5y = 15$?

   • A. $y + 2 = \frac{5}{2}(x - 4)$
   • B. $y - 2 = \frac{5}{2}(x + 4)$
   • C. $y + 2 = -\frac{2}{5}(x - 4)$
   • D. $y + 2 = -\frac{5}{2}(x - 4)$

10. 10. What is the slope of a line that is perpendicular to the line $y = -\frac{1}{3}x + 5$?

    • A. $-\frac{1}{3}$
    • B. 3
    • C. $\frac{1}{3}$
    • D. -3