Graph 3x+6y<=6 3x+y<=6

$3 x + 6 y \leq 6$ $3 x + y \leq 6$

Graph $3 x + 6 y \leq 6$ .

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

Solve for $y$ .

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

$6 y \leq 6 - 3 x$

Divide each term in $6 y \leq 6 - 3 x$ by $6$ and simplify.

Divide each term in $6 y \leq 6 - 3 x$ by $6$ .

$\frac{6 y}{6} \leq \frac{6}{6} + \frac{- 3 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} \leq \frac{6}{6} + \frac{- 3 x}{6}$

Divide $y$ by $1$ .

$y \leq \frac{6}{6} + \frac{- 3 x}{6}$

Simplify the right side.

Simplify each term.

Divide $6$ by $6$ .

$y \leq 1 + \frac{- 3 x}{6}$

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3 x$ .

$y \leq 1 + \frac{3 (- x)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y \leq 1 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y \leq 1 - \frac{x}{2}$

Rearrange terms.

$y \leq - \frac{x}{2} + 1$

Reorder terms.

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

Remove parentheses.

$y \leq - \frac{1}{2} x + 1$

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

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

$m = - \frac{1}{2}$

$b = 1$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 1)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x + 1$ .

$y \leq - \frac{1}{2} x + 1$

Graph $3 x + y \leq 6$ .

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

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

$y \leq 6 - 3 x$

Rearrange terms.

$y \leq - 3 x + 6$

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 $y = m x + b$ .

$m = - 3$

$b = 6$

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

Slope: $- 3$

y-intercept: $(0, 6)$

Slope: $- 3$

y-intercept: $(0, 6)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 3 x + 6$ .

$y \leq - 3 x + 6$

Plot each graph on the same coordinate system.

$3 x + 6 y \leq 6$

$3 x + y \leq 6$

Graph 3x+6y<=6 3x+y<=6

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