Q2A. - Algebra 1

Question

Graph each equation.

$3x-4y=12$

Step-by-Step Solution

Answer

The graph of the equation is:

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 $b$ is the $y$-intercept.

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

Rewrite the equation $3x-4y=12$ in slope-intercept form.

The equation of the straight line is:

  $$\begin{gathered} 3x-4y=12 \\ 3x-4y-3x=12-3x\text{ Subtract }3x\text{ from both sides} \\ \frac{-4y}{-4}=\frac{12-3x}{-4}\text{ Divide both sides by }-4 \\ y=\frac{3}{4}x-3 \end{gathered}$$

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

Step 3. Graph the equation.

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