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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

User Evilruff
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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.

User Eon
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