Question

Graph the line of equation $3x-2y=4$using its slope and y-intercept.

Short answer

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

Step-by-step solution

Step 1. Given information

The equation of a line is given as$2x-3y=4$

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:

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

Hence slope of equation$y=\frac{2}{3}x-\frac{4}{3}$is$\frac{2}{3}$.

Step 3. Identify the y-intercept

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

Step 4. Graph the equation.

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