Pre-Algebra Examples

$x = \frac{3}{4} y - 1$

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 right side.

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Step 1.2.1

Combine $\frac{3}{4}$ and $y$ .

$x = \frac{3 y}{4} - 1$

Step 1.3

Rewrite the equation as $\frac{3 y}{4} - 1 = x$ .

$\frac{3 y}{4} - 1 = x$

Step 1.4

Add $1$ to both sides of the equation.

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

Step 1.5

Multiply both sides of the equation by $\frac{4}{3}$ .

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

Step 1.6

Simplify both sides of the equation.

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Step 1.6.1

Simplify the left side.

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Step 1.6.1.1

Simplify $\frac{4}{3} \cdot \frac{3 y}{4}$ .

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Step 1.6.1.1.1

Cancel the common factor of $4$ .

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Step 1.6.1.1.1.1

Cancel the common factor.

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

Step 1.6.1.1.1.2

Rewrite the expression.

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

Step 1.6.1.1.2

Cancel the common factor of $3$ .

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Step 1.6.1.1.2.1

Factor $3$ out of $3 y$ .

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

Step 1.6.1.1.2.2

Cancel the common factor.

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

Step 1.6.1.1.2.3

Rewrite the expression.

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

Step 1.6.2

Simplify the right side.

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Step 1.6.2.1

Simplify $\frac{4}{3} (x + 1)$ .

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Step 1.6.2.1.1

Apply the distributive property.

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

Step 1.6.2.1.2

Combine $\frac{4}{3}$ and $x$ .

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

Step 1.6.2.1.3

Multiply $\frac{4}{3}$ by $1$ .

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

Step 1.7

Reorder terms.

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

Step 2

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

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

Step 3