Chapter 12, Problem 87CUR

To determine

To write: the equation of line through $\left(-4,-8\right),\left(0,2\right)$

Answer to Problem 87CUR

The equation of line through $\left(-4,-8\right),\left(0,2\right)$ is $4y=10x+8$

Explanation of Solution

Given information:Given points: $\left(-4,-8\right),\left(0,2\right)$

Formula used:

Slope formula:$slope(m)=\frac{changeiny}{change\text{ in }x}$

Equation of line:$y-y_1=m(x-x_1)$

Calculation:

  $\begin{array}{l}m=\frac{changeiny}{change\text{ in }x}\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-(-8)}{0-(-4)}\left[\text{substitute values of }{x}_1,x_2,y_1,y_2\right]\\ m=\frac{10}{4}\\ \text{create equation of line using 1st point}\\ y-y_1=m(x-x_1)\\ y-(-8)=\frac{10}{4}(x-(-4))\left[\text{substituting values of }{x}_1\text{ and }{y}_{{}_1}\right]\\ y+8=\frac{10x+40}{4}\left[\text{multiply}\right]\\ y=\frac{10x+40}{4}-8\left[\text{subtract 8 from both sides}\right]\\ 4y=10x+40-32\left[\text{multiply both sides by 4}\right]\\ 4y=10x+8\end{array}$

Therefore,

The required equation of line is $4y=10x+8$