Algebra Examples

$y \geq - 1$ $5 x + 3 y > - 18$

Step 1

Graph $y \geq - 1$ .

$y \geq - 1$

Step 2

Graph $5 x + 3 y > - 18$ .

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Step 2.1

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

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Step 2.1.1

Solve for $y$ .

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Step 2.1.1.1

Subtract $5 x$ from both sides of the inequality.

$3 y > - 18 - 5 x$

Step 2.1.1.2

Divide each term in $3 y > - 18 - 5 x$ by $3$ and simplify.

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Step 2.1.1.2.1

Divide each term in $3 y > - 18 - 5 x$ by $3$ .

$\frac{3 y}{3} > \frac{- 18}{3} + \frac{- 5 x}{3}$

Step 2.1.1.2.2

Simplify the left side.

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Step 2.1.1.2.2.1

Cancel the common factor of $3$ .

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Step 2.1.1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} > \frac{- 18}{3} + \frac{- 5 x}{3}$

Step 2.1.1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{- 18}{3} + \frac{- 5 x}{3}$

Step 2.1.1.2.3

Simplify the right side.

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Step 2.1.1.2.3.1

Simplify each term.

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Step 2.1.1.2.3.1.1

Divide $- 18$ by $3$ .

$y > - 6 + \frac{- 5 x}{3}$

Step 2.1.1.2.3.1.2

Move the negative in front of the fraction.

$y > - 6 - \frac{5 x}{3}$

Step 2.1.2

Rearrange terms.

$y > - \frac{5 x}{3} - 6$

Step 2.1.3

Reorder terms.

$y > - (\frac{5}{3} x) - 6$

Step 2.1.4

Remove parentheses.

$y > - \frac{5}{3} x - 6$

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 $y = m x + b$ .

$m = - \frac{5}{3}$

$b = - 6$

Step 2.2.2

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

Slope: $- \frac{5}{3}$

y-intercept: $(0, - 6)$

Slope: $- \frac{5}{3}$

y-intercept: $(0, - 6)$

Step 2.3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{5}{3} x - 6$ .

$y > - \frac{5}{3} x - 6$

Step 3

Plot each graph on the same coordinate system.

$y \geq - 1$

$5 x + 3 y > - 18$

Step 4