Answer:
Blue - y=-2
Red-[tex]y=\frac{2}{3}x+2[/tex]
Parallel to Red-[tex]y=\frac{2}{3}x+5[/tex]
Perpendicular to Red- [tex]y=\frac{-3}{2}x+2[/tex]
Step-by-step explanation:
The slope intercept of a line is y=mx +b where
- m is the slope which is calculated as the vertical distance divided by the horizontal distance between two points.
- b is the y-intercept for value on the y-axis for which the line crosses it.
The Blue line intercepts the y-axis at -2 so b=-2. It has no vertical change since it is a horizontal line. This means the slope, m, is 0. m=0. It's equation is y=0x-2
y=0-2 since anything times 0 is 0.
y=-2.
The red line intercepts the y-axis at 2 so b=2. It intercepts the x-axis at (-3,0). Between these two intercepts we can find the slope:
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=0\\y_1=2[/tex] and [tex]x_2=-3\\y_2=0[/tex]
[tex]m=\frac{0-2}{-3-0}[/tex]
[tex]m=\frac{-2}{-3}=\frac{2}{3}[/tex]
The red line has equation [tex]y=\frac{2}{3}x+2[/tex].
Parallel lines have the same slope with a different y-intercept. So we write a line where m=2/3 and b is something else.
[tex]y=\frac{2}{3}x+5[/tex]
Perpendicular lines have a negative reciprocal slope to the original. So we write the line where m/-3/2.
[tex]y=\frac{-3}{2}x+2[/tex]
