Answer:
Hey There!
Let's solve...
We know that the given line is
[tex]y = 4x + 8 \\ [/tex]
Slope is
[tex]m_{g} = 4 \\ [/tex]
The answer is perpendicular to m which is the negative reciprocal of m_g
[tex]m = - \frac{1}{ m_{g} } = - \frac{1}{4} \\ [/tex]
[tex]y = 2 \\ x = 2(2) = - 1 \\ x = 4 - 1 = 3 \\ x = 3[/tex]
The intersection point is
(3,2)
If we substitute the point into
[tex]y = mx + c \\ y = - \frac{1}{4}x + c \\ [/tex]
Now let's solve y intercept...
[tex]2 = - \frac{1}{4}(3) + c \\ \\ c = 2 + \frac{3}{4} \\ [/tex]
[tex] = \frac{8}{4} + \frac{3}{4} \\ \\ = \frac{8 + 3}{4} = \frac{11}{4} [/tex]
Now the required lines are
[tex]y = - \frac{1}{4}x + \frac{11}{4} \\ \\ m = - \frac{1}{4} \\ \\ c = \frac{11}{4} [/tex]
