Algebra Examples

$y \leq \frac{- 3}{2} x + 6$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Move the negative in front of the fraction.

$y \leq - \frac{3}{2} x + 6$

Step 1.1.2

Combine $x$ and $\frac{3}{2}$ .

$y \leq - \frac{x \cdot 3}{2} + 6$

Step 1.1.3

Move $3$ to the left of $x$ .

$y \leq - \frac{3 x}{2} + 6$

Step 1.2

Reorder terms.

$y \leq - (\frac{3}{2} x) + 6$

Step 1.3

Remove parentheses.

$y \leq - \frac{3}{2} x + 6$

Step 2

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

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Step 2.1

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

$m = - \frac{3}{2}$

$b = 6$

Step 2.2

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, 6)$

Slope: $- \frac{3}{2}$

y-intercept: $(0, 6)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{2} x + 6$ .

$y \leq - \frac{3}{2} x + 6$

Step 4