Graph 6x+2y

$6 x + 2 y \leq - 46$

Solve for $y$ .

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Subtract $6 x$ from both sides of the inequality.

$2 y \leq - 46 - 6 x$

Divide each term by $2$ and simplify.

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Divide each term in $2 y \leq - 46 - 6 x$ by $2$ .

$\frac{2 y}{2} \leq \frac{- 46}{2} + \frac{- 6 x}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} \leq \frac{- 46}{2} + \frac{- 6 x}{2}$

Divide $y$ by $1$ .

$y \leq \frac{- 46}{2} + \frac{- 6 x}{2}$

Simplify each term.

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Divide $- 46$ by $2$ .

$y \leq - 23 + \frac{- 6 x}{2}$

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

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Factor $2$ out of $- 6 x$ .

$y \leq - 23 + \frac{2 (- 3 x)}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$y \leq - 23 + \frac{2 (- 3 x)}{2 (1)}$

Cancel the common factor.

$y \leq - 23 + \frac{2 (- 3 x)}{2 \cdot 1}$

Rewrite the expression.

$y \leq - 23 + \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y \leq - 23 - 3 x$

Find the slope and the y-intercept for the boundary line.

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Rewrite in slope-intercept form.

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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 $- 23$ and $- 3 x$ .

$y \leq - 3 x - 23$

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

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

$m = - 3$

$b = - 23$

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

Slope: $- 3$

y-intercept: $(0, - 23)$

Slope: $- 3$

y-intercept: $(0, - 23)$

Slope: $- 3$

y-intercept: $(0, - 23)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 23 - 3 x$ .

$y \leq - 23 - 3 x$

Graph 6x+2y<=-46

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