Question

which equation represents a line which is parallel to the line $5x - y = 6$?

answer
$\circ\\ y = -\frac{1}{5}x + 2$ $\circ\\ y = \frac{1}{5}x + 3$
$\circ\\ y = 5x - 2$ $\circ\\ y = -5x - 1$

Explanation:

Step1: Find slope of given line

Rewrite \(5x - y = 6\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope).
Subtract \(5x\) from both sides: \(-y=-5x + 6\).
Multiply both sides by \(- 1\): \(y = 5x-6\). So the slope of the line \(5x - y = 6\) is \(m = 5\).

Step2: Determine slope of parallel line

Parallel lines have the same slope. So we need to find the equation of the line with slope \(m = 5\) from the given options.

Check the slopes of the options:

• For \(y=-\frac{1}{5}x + 2\), slope \(m=-\frac{1}{5}\).
• For \(y=\frac{1}{5}x + 3\), slope \(m=\frac{1}{5}\).
• For \(y = 5x-2\), slope \(m = 5\).
• For \(y=-5x - 1\), slope \(m=-5\).

Answer:

\(y = 5x-2\) (the option with \(y = 5x-2\))