Answer:
Parallel line - y=6x+9
Perpendicular line - y=-1/6x +4
Step-by-step explanation:
Parallel lines have a slope that is equal to the origninal equation. You use the y-y1=m(x-x1) equation. In this case, your y1 is 3 and your x1 is -1. Plug these into the equation along with your slope of 6.
y-y1=m(x-x1)
y-3=6(x-(-1))
y-3=6(x+1)
y-3=6x+6 - Distribute
+3 +3 - Add 3 to both sides
y=6x+9
For perpendicular lines, the slope is the negative reciprocal of the given slope. In this case, the slope is -1/6. Your y1 is 4 and your x1 is 0.
y-y1=m(x-x1)
[tex]y - 4 = - \frac{1}{6} (x - 0)[/tex]
Distribute:
[tex]y - 4 = - \frac{1}{6} x[/tex]
+4 +4
Add 4 to both sides:
[tex]y = - \frac{1}{6} x + 4[/tex]
