Question

Graph each equation.

$\mathbf{6}\mathit{x}\mathbf{-}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{16}$

Short answer

The graph of the equation is:

Step-by-step solution

Step 1. State the concept of slope-intercept of an equation.

The slope-intercept form of a linear equation is $y=mx+b$, where $m$is the slope and is the$y$-intercept.

Step 2. Write equation of a line in slope-intercept form.

Rewrite the equation $6x-4y=16$in slope-intercept form.

The equation of the straight line is:

localid="1647498079774" $\begin{array}{l}6x-4y=16\\ 6x-4y-6x=16-6x\text{Subtract6}x\text{frombothsides}\\ \frac{-4y}{-4}=\frac{-6x+16}{-4}\text{Dividebothsidesby}-4\\ y=\frac{3}{2}x-4\end{array}$

The slope is $m=\frac{3}{2}$ and the y-intercept is $(0,-4)$.

Step 3. Graph the equation.

To graph the equation, plot the $y$-intercept $(0,-4)$. The slope is $\frac{\text{rise}}{\text{run}}=\frac{3}{2}$. From $(0,-4)$, move up 3 units and right 2 units. Plot the point. Draw the line through the two points.