# How do you write an equation in standard form for a line passes through (2, –3) and is perpendicular to y = 4x + 7?

Jun 6, 2015

Answer: the equation of the line is $y = - \frac{1}{4} x - \frac{5}{2}$

Explanation: We have two lines: ${L}_{1}$ defined by the equation $y = a x + b$ and ${L}_{2}$ defined by the equation $y = 4 x + 7$ $\implies$ The slope of the line ${L}_{2}$ is $4$.

We know that, If ${L}_{1}$ is perpendicular to ${L}_{2}$, then the slope of ${L}_{1}$ is the inverse reciprocal of the slope of ${L}_{2}$. Therefore, the slope of ${L}_{1}$ is $- \frac{1}{4}$.

So, the equation of ${L}_{1}$ is $- \frac{1}{4} x + b$

The line ${L}_{1}$ contains the point $A \left(2 , - 3\right)$, therefore we have the following equation: $- 3 = - \frac{1}{4} \cdot 2 + b$ $\implies$ $b = - \frac{5}{2}$

Therefore, the equation of ${l}_{1}$ is $y = - \frac{1}{4} x - \frac{5}{2}$