Question

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

Short answer

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

Step-by-step solution

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,

role="math" localid="1646375934175" $$\begin{gathered} y=mx+c \\ \Rightarrow 5=-3(-2)+c \\ \Rightarrow 5=6+c \\ \Rightarrow c=5-6 \\ \Rightarrow c=-1 \end{gathered}$$

The equation of the line isrole="math" localid="1646375948929" $y=-3x-1$.