Graph -6x+2y<=42

$- 6 x + 2 y \leq 42$

Step 1

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

Solve for $y$ .

Add $6 x$ to both sides of the inequality.

$2 y \leq 42 + 6 x$

Divide each term in $2 y \leq 42 + 6 x$ by $2$ and simplify.

Divide each term in $2 y \leq 42 + 6 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{42}{2} + \frac{6 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{42}{2} + \frac{6 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{42}{2} + \frac{6 x}{2}$

Simplify the right side.

Simplify each term.

Divide $42$ by $2$ .

$y \leq 21 + \frac{6 x}{2}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 x$ .

$y \leq 21 + \frac{2 (3 x)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y \leq 21 + \frac{2 (3 x)}{2 (1)}$

Cancel the common factor.

$y \leq 21 + \frac{2 (3 x)}{2 \cdot 1}$

Rewrite the expression.

$y \leq 21 + \frac{3 x}{1}$

Divide $3 x$ by $1$ .

$y \leq 21 + 3 x$

Rearrange terms.

$y \leq 3 x + 21$

Step 2

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

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

$y = m x + b$

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

$m = 3$

$b = 21$

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

Slope: $3$

y-intercept: $(0, 21)$

Slope: $3$

y-intercept: $(0, 21)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $3 x + 21$ .

$y \leq 3 x + 21$

Step 4

Graph -6x+2y<=42

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