Chapter 8.6, Problem 2E

To determine

Describe the steps you would use to write an equation of the line that passes through the given points.

Answer to Problem 2E

The equation of the line passing through the given points would be $y=3x+9$ .

Explanation of Solution

Given:

Two points on a line: $(-2,3)\text{and }(0,9)$

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 $y=mx+b$ , where m represents slope of line and b represents the y -intercept.

Calculation:

Our first step is to find the slope of line passing through the given points.

Let point $(-2,3)=(x_1,y_1)\text{and (}0,9\text{)}=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

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

We can see from our given points that the y -intercept is $(0,9)$ .

Our next step is to substitute the value of slope and y -intercept in slope-intercept form of equation as shown below:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=3\cdot x+9\left(\text{Substituting }m=3\text{ and }b=9\right)\\ y=3x+9\end{array}$

Therefore, the equation of the line passing through the given points would be $y=3x+9$ .