Question

What is an equation of the line that passes though the point (-4,7) and is perpendicular to the line y=4x+2?

Answer 1

If the line is perpendicular to the line with equation y = 4x + 2

Then

$\begin{gathered} \text{If m}_{1\text{ }}slope\text{ of equation of the of line y = 4x + 2} \\ m_{2\text{ }}---\text{ slope of the new line} \end{gathered}$$\begin{gathered} \text{then } \\ m_{2\text{ }}=\text{ }\frac{-1}{m_1} \\ m_1=\text{ 4} \\ \text{Thus, } \\ m_2=\text{ -}\frac{1}{4} \end{gathered}$

Using y = mx + c, the intercept is obtain by substituting for x, y and m

$\begin{gathered} y\text{ = mx + c} \\ y\text{ = 7, x = -4 ,m = }\frac{-1}{4} \\ 7\text{ = }\frac{-1}{4}\times\text{ -4 + c} \\ 7\text{ = 1 + c } \\ c\text{ = 7 -1} \\ c\text{ = 6} \end{gathered}$

To write the equation of the new line then, we substitute for m and c in y = mx + c

$\begin{gathered} y\text{ = }\frac{-1}{4}x\text{ + 6} \\ \\ OR \\ 4y\text{ = -x + 24 ( when you multiply through by 4)} \end{gathered}$