Question

question
which equation represents a line which is parallel to the line $x - 7y = -21$?

answer
$\circ\\ y = \frac{1}{7}x + 5$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ $\circ\\ y = 7x + 4$
$\circ\\ y = -7x - 8$ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ $\circ\\ y = -\frac{1}{7}x - 3$

Explanation:

Step1: Convert to slope - intercept form

To find the slope of the line \(x - 7y=- 21\), we convert it to the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
Starting with \(x-7y=-21\), we isolate \(y\):
Subtract \(x\) from both sides: \(-7y=-x - 21\)
Divide each term by \(- 7\): \(y=\frac{1}{7}x + 3\)
So the slope of the line \(x - 7y=-21\) is \(m=\frac{1}{7}\).

Step2: Determine the slope of parallel lines

Parallel lines have the same slope. So we need to find the equation of the line with slope \(\frac{1}{7}\) from the given options.

• For the line \(y = \frac{1}{7}x+5\), the slope \(m=\frac{1}{7}\).
• For the line \(y = 7x + 4\), the slope \(m = 7\).
• For the line \(y=-7x - 8\), the slope \(m=-7\).
• For the line \(y=-\frac{1}{7}x - 3\), the slope \(m =-\frac{1}{7}\).

Answer:

\(y=\frac{1}{7}x + 5\) (the first option)