Chapter 13.6, Problem 14WE

To determine

To find:Slope and y-intercept of each line. Plot the y-intercept. Then using the slope, plot one more point. Finally graph the line.

Answer to Problem 14WE

The slope is 2 and the y-intercept is 3.

Explanation of Solution

Given information:Line: $y=2x+3$ .

Concept Used:A line with the equation $y=mx+b$ has slope $m$ and $y\text{-intercept }b$ .

Calculation:

Comparing the line $y=2x+3$ with equation $y=mx+b$ :

The slope of line, $m=2$ and the $y\text{-intercept, }b=3$

Since, $y\text{-intercept is 3}$

So, one point is $(x_1,y_1)\equiv (0,3)$

For one more point, using $m=\frac{y_2-y_1}{x_2-x_1}=2$ :

Let taking $x_2=1$ , then

  $\begin{array}{l}\frac{y_2-3}{1-0}=2\\ \Rightarrow y_2-3=2\\ \Rightarrow y_2=2+3\\ \Rightarrow y_2=5\end{array}$

So, second point is $(x_2,y_2)\equiv (1,5)$

Hence, the slope is 2 and the y-intercept is 3.

Graph: