Answer:
Blue line is y=-2
Red line is [tex]y=\frac{2}{3}x+2[/tex].
Perpendicular to red is [tex]y=-\frac{3}{2}x+2[/tex].
Parallel to red is [tex]y=\frac{2}{3}x+5[/tex]
Step-by-step explanation:
The blue line is a horizontal line through the y-axis. These lines have no slope and are written as y=0x-2 since -2 is the y-intercept. We simplify and y=-2.
The red line has a slope of 2/3 since it rises 2 units for every 3 units it runs from point to point. It has a y-intercept at 2 on the y-axis. The equation in slope-intercept is y=mx +b. We substitute. [tex]y=\frac{2}{3}x+2[/tex]
To write a parallel line, we use the same slope and choose a different y-intercept. Parallel to red is [tex]y=\frac{2}{3}x+5[/tex]
To write a perpendicular line, we find the negative reciprocal of the slope which is -3/2. Perpendicular to red is [tex]y=-\frac{3}{2}x+2[/tex].
