Pre-Algebra Examples

$- \frac{9}{4} x + 3 y = 18$

Step 1

Rewrite in slope-intercept form.

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Step 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 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $x$ and $\frac{9}{4}$ .

$- \frac{x \cdot 9}{4} + 3 y = 18$

Step 1.2.1.2

Move $9$ to the left of $x$ .

$- \frac{9 x}{4} + 3 y = 18$

Step 1.3

Add $\frac{9 x}{4}$ to both sides of the equation.

$3 y = 18 + \frac{9 x}{4}$

Step 1.4

Divide each term in $3 y = 18 + \frac{9 x}{4}$ by $3$ and simplify.

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Step 1.4.1

Divide each term in $3 y = 18 + \frac{9 x}{4}$ by $3$ .

$\frac{3 y}{3} = \frac{18}{3} + \frac{\frac{9 x}{4}}{3}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $3$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{18}{3} + \frac{\frac{9 x}{4}}{3}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{3} + \frac{\frac{9 x}{4}}{3}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Divide $18$ by $3$ .

$y = 6 + \frac{\frac{9 x}{4}}{3}$

Step 1.4.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = 6 + \frac{9 x}{4} \cdot \frac{1}{3}$

Step 1.4.3.1.3

Cancel the common factor of $3$ .

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Step 1.4.3.1.3.1

Factor $3$ out of $9 x$ .

$y = 6 + \frac{3 (3 x)}{4} \cdot \frac{1}{3}$

Step 1.4.3.1.3.2

Cancel the common factor.

$y = 6 + \frac{3 (3 x)}{4} \cdot \frac{1}{3}$

Step 1.4.3.1.3.3

Rewrite the expression.

$y = 6 + \frac{3 x}{4}$

Step 1.5

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

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Step 1.5.1

Reorder $6$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} + 6$

Step 1.5.2

Reorder terms.

$y = \frac{3}{4} x + 6$

Step 2

Using the slope-intercept form, the slope is $\frac{3}{4}$ .

$m = \frac{3}{4}$

Step 3