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

• 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.

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

`(-2y)/(-2)=(-x+4)/(-2)`

`y=(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.