Graph 3y<=7x-21

$3 y \leq 7 x - 21$

Step 1

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

Divide each term in $3 y \leq 7 x - 21$ by $3$ and simplify.

Divide each term in $3 y \leq 7 x - 21$ by $3$ .

$\frac{3 y}{3} \leq \frac{7 x}{3} + \frac{- 21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \leq \frac{7 x}{3} + \frac{- 21}{3}$

Divide $y$ by $1$ .

$y \leq \frac{7 x}{3} + \frac{- 21}{3}$

Simplify the right side.

Divide $- 21$ by $3$ .

$y \leq \frac{7 x}{3} - 7$

Reorder terms.

$y \leq \frac{7}{3} x - 7$

Step 2

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

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

$m = \frac{7}{3}$

$b = - 7$

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

Slope: $\frac{7}{3}$

y-intercept: $(0, - 7)$

Slope: $\frac{7}{3}$

y-intercept: $(0, - 7)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{7}{3} x - 7$ .

$y \leq \frac{7}{3} x - 7$

Step 4