Chapter 8.6, Problem 15E

To determine

To write:

Anequation of the line that passes through the given points.

Answer to Problem 15E

The equation of the line passing through the given pointswould be $y=2x+9$ .

Explanation of Solution

Given:

Two points on a line: $(0,9)\text{and }(3,15)$

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 $(0,9)=(x_1,y_1)\text{and }(3,15)=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{15-9}{3-0}\\ m=\frac{6}{3}\\ m=2\end{array}$

To write our equation, we will substitute the value of slope and coordinates of point $(0,9)$ in point-slope form of equation as shown below:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\left(\text{Point-slope form of equation}\right)\\ y-9=2\left(x-0\right)\left(\text{Substituting given values}\right)\\ y-9=2x\\ y-9+9=2x+9\\ y=2x+9\end{array}$

Therefore, the equation of the line passing through the given points would be $y=2x+9$ .