Question

Write the equation of the line that goes through the point (−9, −4) and is parallel to the line −x + 3y = −0.5

Answer 1

Answer:

$y = \frac{1}{3}x -1$

Explanation:

Given

Parallel to: $-x + 3y = -0.5$

Passes through (-9,-4)

Required

Determine the line equation

First, we calculate the slope (m) of the said line

$-x + 3y = -0.5$

Make y the subject

$3y = x - 0.5$

Divide through by 3

$y = \frac{1}{3}x - \frac{0.5}{3}$

An equation has the general form:

$y = mx + b$

Where

$m = slope$

So:

$m = \frac{1}{3}$

Because the required line is parallel to $-x + 3y = -0.5$, then they have the same slope of $m = \frac{1}{3}$

Next, is to calculate the line equation using:

$y = m(x - x_1) + y_1$

Where

$m = \frac{1}{3}$

$(x_1,y_1) = (-9,-4)$

This gives:

$y = \frac{1}{3}(x -(-9)) + (-4)$

$y = \frac{1}{3}(x +9) -4$

Open bracket

$y = \frac{1}{3}x +3 -4$

$y = \frac{1}{3}x -1$