Algebra Examples

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

Step 1

Graph $y \leq x + 1$ .

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Step 1.1

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

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Step 1.1.1

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 1.1.2

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

$m = 1$

$b = 1$

Step 1.1.3

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

Slope: $1$

y-intercept: $(0, 1)$

Slope: $1$

y-intercept: $(0, 1)$

Step 1.2

Graph a solid line, then shade the area below the boundary line since $y$ is less than $x + 1$ .

$y \leq x + 1$

Step 2

Graph $y < - \frac{x}{2} - 1$ .

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Step 2.1

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

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Step 2.1.1

Reorder terms.

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

Step 2.1.2

Remove parentheses.

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

Step 2.2

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

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Step 2.2.1

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

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

$b = - 1$

Step 2.2.2

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: $(0, - 1)$

Step 2.3

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

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

Step 3

Plot each graph on the same coordinate system.

$y \leq x + 1$

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

Step 4