Question

Which of these lines is parallel to y = 5x − 9? Select all that apply.
A. y = −15
x + 9
B. y = 5x + 9
C. 2y + 5x = 9
D. 2y − 10x = 9
E. y − 6 = 5(x − 9)
F. y − 6 = −5(x − 9)

Answer 1

To determine which lines are parallel to the line \( y = 5x - 9 \), we need to recognize that parallel lines have the same slope. The slope of the given line \( y = 5x - 9 \) is 5.

Now, let's analyze each option to find the slope:

A: \( y = -15x + 9 \)
- Slope is -15 (not parallel).

B: \( y = 5x + 9 \)
- Slope is 5 (parallel).

C: \( 2y + 5x = 9 \)
- Rearranging to slope-intercept form:
\[
2y = -5x + 9 \\
y = -\frac{5}{2}x + \frac{9}{2}
\]
- Slope is -\(\frac{5}{2}\) (not parallel).

D: \( 2y - 10x = 9 \)
- Rearranging to slope-intercept form:
\[
2y = 10x + 9 \\
y = 5x + \frac{9}{2}
\]
- Slope is 5 (parallel).

E: \( y - 6 = 5(x - 9) \)
- Rearranging to slope-intercept form:
\[
y - 6 = 5x - 45 \\
y = 5x - 39
\]
- Slope is 5 (parallel).

F: \( y - 6 = -5(x - 9) \)
- Rearranging to slope-intercept form:
\[
y - 6 = -5x + 45 \\
y = -5x + 51
\]
- Slope is -5 (not parallel).

The lines that are parallel to \( y = 5x - 9 \) are:
- **B.** \( y = 5x + 9 \)
- **D.** \( 2y - 10x = 9 \)
- **E.** \( y - 6 = 5(x - 9) \)

So the correct answers are **B, D, and E.**