Graph 3x+4y<=12

$3 x + 4 y \leq 12$

Step 1

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$4 y \leq 12 - 3 x$

Divide each term in $4 y \leq 12 - 3 x$ by $4$ and simplify.

Divide each term in $4 y \leq 12 - 3 x$ by $4$ .

$\frac{4 y}{4} \leq \frac{12}{4} + \frac{- 3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \leq \frac{12}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y \leq \frac{12}{4} + \frac{- 3 x}{4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

$y \leq 3 + \frac{- 3 x}{4}$

Move the negative in front of the fraction.

$y \leq 3 - \frac{3 x}{4}$

Rearrange terms.

$y \leq - \frac{3 x}{4} + 3$

Reorder terms.

$y \leq - (\frac{3}{4} x) + 3$

Remove parentheses.

$y \leq - \frac{3}{4} x + 3$

Step 2

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 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{4} x + 3$ .

$y \leq - \frac{3}{4} x + 3$

Step 4