Chapter 3, Problem 37SGR

To determine

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

Answer to Problem 37SGR

Graph of the given equation:

  

Slope of the line is -3 y-intercept of line is 5.

Explanation of Solution

Given information: Linear equation $y=-3x+5$

Solution:

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

Plugging x=0 in given equation

  $\begin{array}{l}y=-3\left(0\right)+5\\ \Rightarrow y=5\end{array}$

We got first coordinate (0, 5).

Now, plugging x=2 in given equation

  $\begin{array}{l}y=-3\left(2\right)+5\\ \Rightarrow y=-6+5\\ \Rightarrow y=-1\end{array}$

So, we got second coordinate (2,-1).

Draw a line by joining the points $\left(0,5\right)$ and $(2,-1)$

  

From the graph, we can see that line crosses y-axis at 5. Therefore, y-intercept is 5.

Now, if we go 3 units down and 1 unit right, we get another coordinate (1, 2).

So the slope will be

  $\frac{Rise}{Run}$

  $=\frac{5-2}{0-1}=-\frac{3}{1}$

Therefore, slope of the line is -3.