Question

Graph the line of equation $3x-4y=8$using its slope and y-intercept.

Short answer

The slope of equation is $\frac{3}{4}$and the y-intercept is $(0,-2)$.The graph is plotted below:

Step-by-step solution

Step 1. Given information

The equation of a line is given as $3x-4y=8$.

Step 2. Identify the slope

The slope intercept form is as $y=mx+b$where $m$is the slope and $(0,b)$is the y-intercept.

The given equation is converted into slope intercept form as:

$$\begin{gathered} 3x-4y=8 \\ -4y=-3x+8 \\ y=\frac{3}{4}x-2 \end{gathered}$$

Hence the slope is$\frac{3}{4}$.

Step 3. Identify the y-intercept

The y-intercept of equation$y=\frac{3}{4}x-2$is$(0,-2)$.

Step 4. Graph the equation 3x-4y=8

The graph of equation $3x-4y=8$with slope $\frac{3}{4}$and y-intercept $(0,-2)$is plotted below: