Question

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

$4x-3y=12$

Short answer

The graph of the line is

Step-by-step solution

Step 1. Given information

The equation of line

$4x-3y=12$...................Equation (1)

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

Rewrite equation (1)

$$\begin{gathered} 4x-12=3y \\ 3y=4x-12 \\ y=\frac{1}{3}\left(4x-12\right) \end{gathered}$$

$y=\frac{4}{3}x-4$...............equation(2)

By comparing the given equation (2) with standard equation of line

$y=mx+c$

We get

$$\begin{gathered} m=\frac{4}{3} \\ c=-4 \end{gathered}$$

That means slope is $\frac{4}{3}$and y-intercept is (0, -4)

Step 3. Plot the y-intercept 

Plot the point (0, -4) in a rectangular coordinate system

Step 4. Identify the rise over the run 

Slope of the line$\frac{4}{3}$

$m=\frac{4}{3}$

So rise is 4 and run is 3

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

Rise is 4 and run is 3

So mark another point on the same graph at a distance of 3 unit in right direction along x-axis and 4 unit in upward direction along y-axis from first point

Step 6. Connect both points and extend the line. 

The graph of the line is