Algebra Examples

$x + y \leq 3$

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the inequality.

$y \leq 3 - x$

Step 1.2

Rearrange terms.

$y \leq - x + 3$

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 $y = m x + b$ .

$m = - 1$

$b = 3$

Step 2.3

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

Slope: $- 1$

y-intercept: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Step 3

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

$y \leq - x + 3$

Step 4