Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with slope $-3$ containing the point $(-2, 5)$. 

Step-by-Step Solution

Answer

The equation of the line is $y=-3x-1$.

Step 1. Given Information

Slope of the line$\left(m\right)$ is $-3$.

The line passes through the point $(-2, 5)$.

We need to find the equation of the line.

Step 2. Finding the equation of the line

Equation of line in standard format is $y=mx+c$ where $m$ is the slope of the line and $c$ is the intercept of the line.

Substituting the values in the equation we get,

$$\begin{gathered} y=mx+c \\ \Rightarrow 5=-3(-2)+c \\ \Rightarrow 5=6+c \\ \Rightarrow c=5-6 \\ \Rightarrow c=-1 \end{gathered}$$

The equation of the line is  $y=-3x-1$.