Chapter 13.6, Problem 16WE

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 16WE

The slope is $\frac{3}{4}$ and the y-intercept is 1.

Explanation of Solution

Given information:Line: $y=\frac{3}{4}x+1$ .

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

Calculation:

Comparing the line $y=\frac{3}{4}x+1$ with equation $y=mx+b$ :

The slope of line, $m=\frac{3}{4}$ and the $y\text{-intercept, }b=1$

Since, $y\text{-intercept is 1}$

So, one point is $(x_1,y_1)\equiv (0,1)$

For one more point, using $m=\frac{y_2-y_1}{x_2-x_1}=\frac{3}{4}$ :

Let taking $x_2=4$ , then

  $\begin{array}{l}\frac{y_2-1}{4-0}=\frac{3}{4}\\ \Rightarrow y_2-1=\frac{3}{4}\times 4\\ \Rightarrow y_2=3+1\\ \Rightarrow y_2=4\end{array}$

So, second point is $(x_2,y_2)\equiv (4,4)$

Hence, the slope is $\frac{3}{4}$ and the y-intercept is 1.

Graph: