Question

In the following exercises, graph the line of each equation using its slope and y-intercept.

$y=-\frac{2}{5}x+3$

Short answer

The graph of the line is

Step-by-step solution

Step 1. Given information

The equation of line

$y=-\frac{2}{5}x+3$...................Equation (1)

Step 2. Identify the slope and y-intercept of the line

By comparing the given equation (1) with standard equation of line

$y=mx+c$

We get

$$\begin{gathered} m=-\frac{2}{5} \\ c=3 \end{gathered}$$

That means slope is $-\frac{2}{5}$and y-intercept is (0, 3)

Step 3. Plot the y-intercept

Plot the point (0, 3) in a rectangular coordinate system

Step 4. Identify the rise over the run

Slope of the line$-\frac{2}{5}$

$m=-\frac{2}{5}$

So rise is -2 and run is 5

Step 5. Count out the rise and run to mark the second point 

Rise is -2 and run is 5

So mark another point on the same graph at a distance of 5 unit in right direction along x-axis and 2 unit in downward direction along y-axis from first point

Step 6. Connect both points and extend the line.

The graph of the line is