Given the line
[tex]y=2x+4[/tex]The line is expressed in slope-intercept form:
[tex]y=mx+b[/tex]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
[tex]y=2x+1[/tex]2) For perpendicular lines, the slope of a line perpendicular to another is the inverse negative of the slope of the line.
So let
[tex]y=nx+c[/tex]Represent the equation of the line perpendicular to the given one. The relationship between their slopes can be expressed as:
[tex]n=-\frac{1}{m}[/tex]The slope of the line is m=2 so the slope of the perpendicular line is
[tex]n=-\frac{1}{2}[/tex]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
[tex]y=-\frac{1}{2}x+10[/tex]The correct option is the third one.
