Chapter 8.6, Problem 16E

To determine

To write:

Anequation of the line that passes through the given points.

Answer to Problem 16E

The equation of the line passing through the given pointswould be $y=-\frac{5}{4}x-6$ .

Explanation of Solution

Given:

Two points on a line: $(0,-6)\text{and }(8,-16)$

Concept used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

The equation of a line in point-slope form is $y-y_1=m\left(x-x_1\right)$ , where m represents slope of line and $\left(x_1,y_1\right)$ represents a point on the line.

Calculation:

First of all, we will find the slope of line passing through the given points.

Let point $(0,-6)=(x_1,y_1)\text{and }(8,-16)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-16-(-6)}{8-0}\\ m=\frac{-16+6}{8}\\ m=\frac{-10}{8}\\ m=-\frac{5}{4}\end{array}$

To write our equation, we will substitute the value of slope and coordinates of point $(0,-6)$ in point-slope form of equation as shown below:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\left(\text{Point-slope form of equation}\right)\\ y-(-6)=-\frac{5}{4}\left(x-0\right)\left(\text{Substituting given values}\right)\\ y+6=-\frac{5}{4}x\\ y+6-6=-\frac{5}{4}x-6\\ y=-\frac{5}{4}x-6\end{array}$

Therefore, the equation of the line passing through the given points would be $y=-\frac{5}{4}x-6$ .