Chapter 3, Problem 38SGR

To determine

To graph the equation then state the slope and y- intercept of line.

Answer to Problem 38SGR

Graph of the given equation:

  

Slope of the line is $\frac{1}{2}$ .

y-intercept of line is 1.

Explanation of Solution

Given information: Linear equation $y=\frac{1}{2}x+1.$

Solution:

In order to graph the line, we need to get two points.

Plugging x=0 in given equation

  $\begin{array}{l}y=\frac{1}{2}(0)+1\\ \Rightarrow y=1\end{array}$

We got first coordinate (0, 1).

Now, plugging x=2 in given equation

  $\begin{array}{l}y=\frac{1}{2}(2)+1\\ \Rightarrow y=2\end{array}$

So, we got second coordinate (2, 2).

Draw a line by joining the points $\left(0,1\right)$ and $(2,2)$

  

From the graph, we can see that line crosses y-axis at 1. Therefore, y-intercept is 1.

Now, if we go 1 units up and 2 units right, we get another coordinate (2, 2).

So the slope will be

  $\frac{Rise}{Run}=\frac{1-(2)}{0-2}=\frac{1}{2}$ .

Therefore, slope of the line is $\frac{1}{2}$ .