Chapter 3, Problem 36SGR

To determine

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

Answer to Problem 36SGR

Graph of the given equation:

  

y-intercept of line is -2.

Slope of the line is 4.

Explanation of Solution

Given information: Linear equation $y=4x-2.$

Solution:

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

Plugging x=0 in given equation

  $\begin{array}{l}y=4\left(0\right)-2\\ \Rightarrow y=-2\end{array}$

We got first coordinate (0, -2).

Now, plugging x=2 in given equation

  $\begin{array}{l}y=4\left(2\right)-2\\ \Rightarrow y=8-2\\ \Rightarrow y=6\end{array}$

So, we got second coordinate (2, 6).

Draw a line by joining the points $\left(0,-2\right)$ and $(2,6)$

  

From the graph, we can see that line crosses y-axis at -2. Therefore, y-intercept is -2.

Now, if we go 4 units upward and 1 unit right, we get another coordinate (1, 2).

So the slope will be

  $\frac{Rise}{Run}$

  $=\frac{-2-2}{0-1}=\frac{-4}{-1}=4$

Therefore, slope of the line is 4.