Question

Find an equation of the line with slope $5$containing the point $\left(2,-4\right).$

Short answer

The equation of a line with a slope$5$and point$\left(2,-4\right)$is$y=5x-14.$

Step-by-step solution

Step 1. Given Information 

The given point is $\left(2,-4\right)$and the slope is $5.$

We have to find an equation of a line.

Step 2. Finding the equation

To find the equation of a line, we will use the point-slope formula which is $y-y_1=m\left(x-x_1\right).$

Here,$m=5\mathrm{and}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=\left(2,-4\right)$

$$\begin{gathered} y-\left(-4\right)=5\left(x-2\right) \\ y+4=5x-10 \\ y=5x-14 \end{gathered}$$

So, the equation of a line is$y=5x-14.$