Graph -3x+4y=12

$- 3 x + 4 y = 12$

Step 1

Solve for $y$ .

Add $3 x$ to both sides of the equation.

$4 y = 12 + 3 x$

Divide each term in $4 y = 12 + 3 x$ by $4$ and simplify.

Divide each term in $4 y = 12 + 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{12}{4} + \frac{3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{12}{4} + \frac{3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{12}{4} + \frac{3 x}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$y = 3 + \frac{3 x}{4}$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $3$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} + 3$

Reorder terms.

$y = \frac{3}{4} x + 3$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

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

$b = 3$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{3}{4}$

y-intercept: $(0, 3)$

Slope: $\frac{3}{4}$

y-intercept: $(0, 3)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Write in $y = m x + b$ form.

Reorder $3$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} + 3$

Reorder terms.

$y = \frac{3}{4} x + 3$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 3 \\ 4 & 6 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $\frac{3}{4}$

y-intercept: $(0, 3)$

$\begin{array}{c} x & y \\ 0 & 3 \\ 4 & 6 \end{array}$

Step 6

Graph -3x+4y=12

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