Question

what line is perpendicular to the line y = 2x+4 ? what line is parallel to the line y+2xt4? Options1) y=2x+12) y=1/2x+63) y=-1/2x+104) y=-2x+3

Answer 1

Given the line

`y=2x+4`

The line is expressed in slope-intercept form:

`y=mx+b`

Where

m is the slope

b is the y-intercept

1) Any line that has the same slope as this line will be parallel to it.

The slope of the line is m=2

From the given options, the only one that has the same slope as the given line is the first one

`y=2x+1`

2) For perpendicular lines, the slope of a line perpendicular to another is the inverse negative of the slope of the line.

So let

`y=nx+c`

Represent the equation of the line perpendicular to the given one. The relationship between their slopes can be expressed as:

`n=-(1)/(m)`

The slope of the line is m=2 so the slope of the perpendicular line is

`n=-(1)/(2)`

A line with slope -1/2 will be perpedicular to the given one. Looking at the options, the line that can be perpendicular to this one is

`y=-(1)/(2)x+10`

The correct option is the third one.