Answer:
- parallel: y = 1/2x +3
- perpendicular: y = -2x +1
Explanation:
A parallel line will have the same slope as the line on the graph. A perpendicular line will have a slope that is the opposite reciprocal of the slope of the graphed line.
Slope of graphed line
The line on the graph rises 1 grid square for each run of 2 grid squares to the right. Its slope is ...
m = rise/run = 1/2
Slope of perpendicular line
The opposite reciprocal of this slope is ...
-1/(1/2) = -2
A perpendicular line will have a slope of -2.
Slope-intercept form
The slope-intercept form of the equation for a line is ...
y = mx +b
where the slope is m and b is the y-intercept. For the purpose here, we don't care about the y-intercepts of any of the lines. We only care about the slope: the coefficient of x.
This means the equations we're looking for are of the form ...
parallel line: y = 1/2x + b
perpendicular line: y = 2x +b . . . . . for some constant b
Parallel line
Of the equations offered, the only one with an x-coefficient of 1/2 is ...
y = 1/2x +3
Perpendicular line
Of the equations offered, the only one with an x-coefficient of -2 is ...
y = -2x +1