Question

Write the equation of the line perpendicular to y = 4x+7 that passes through the point (-3,5).

Answer 1

In general, if two lines are perpendicular, the product of their slopes is equal to -1. Let m be the slope of the line we are trying to find, notice that the slope of the given line is 4; therefore,

$\begin{gathered} m\cdot4=-1 \\ \Rightarrow m=-\frac{1}{4} \end{gathered}$

The equation of the line we need to find is -1/4.

Given the slope and a point on a line, we can find the equation of such line using the formula below

$\begin{gathered} (x_1,y_1)\to\text{ point on the line} \\ m\to\text{slope of the line} \\ y-y_1=m(x-x_1) \end{gathered}$

In our case,

$\begin{gathered} (-3,5),m=-\frac{1}{4} \\ \Rightarrow y-5=-\frac{1}{4}(x-(-3)) \\ \Rightarrow y-5=-\frac{1}{4}(x+3) \\ \Rightarrow y-5=-\frac{1}{4}x-\frac{3}{4} \\ \Rightarrow y=-\frac{1}{4}x+\frac{17}{4} \end{gathered}$

The answer is y=-x/4+17/4