Algebra Examples

$6 x - 5 \leq 11 x + y$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite so $y$ is on the left side of the inequality.

$11 x + y \geq 6 x - 5$

Step 1.2

Move all terms not containing $y$ to the right side of the inequality.

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Step 1.2.1

Subtract $11 x$ from both sides of the inequality.

$y \geq 6 x - 5 - 11 x$

Step 1.2.2

Subtract $11 x$ from $6 x$ .

$y \geq - 5 x - 5$

Step 2

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

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Step 2.1

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

$y = m x + b$

Step 2.2

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

$m = - 5$

$b = - 5$

Step 2.3

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

Slope: $- 5$

y-intercept: $(0, - 5)$

Slope: $- 5$

y-intercept: $(0, - 5)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- 5 x - 5$ .

$y \geq - 5 x - 5$

Step 4