Question

Line m has the equation y = 1/2x - 4
If lines m and n are parallel to each other, which of the following equations could represent line n?
2x+y=4
2x-y=4
X+2y=4
X-2y=4

Answer 1

Answer:

• As the slopes of both lines 'm' and 'n' are the same.

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

Step-by-step explanation:

We know that the slope-intercept of line equation is  

$y=mx+b$

Where m is the slope and b is the y-intercept

Given the equation of the line m

y = 1/2x - 4

comparing with the slope-intercept form of the line equation

y  = mx + b

Therefore,

The slope of line 'm' will be = 1/2

We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2

Checking the equation of the line 'n'

$x-2y=4$

solving for y to writing the equation in the slope-intercept form and determining the slope

$x-2y=4$

Add -x to both sides.

$x - 2y + (-x) = 4+(-x)$

$-2y = 4 - x$

Divide both sides by -2

$\frac{-2y}{-2}=\frac{-x+4}{-2}$

$y=\frac{1}{2}x-2$

comparing ith the slope-intercept form of the line equation

Thus, the slope of the line 'n' will be: 1/2

• As the slopes of both lines 'm' and 'n' are the same.

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.