Precalculus Examples

$\frac{y}{3} - 2 x + 4 = 5$

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

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Add $2 x$ to both sides of the equation.

$\frac{y}{3} + 4 = 5 + 2 x$

Step 1.2.2

Subtract $4$ from both sides of the equation.

$\frac{y}{3} = 5 + 2 x - 4$

Step 1.2.3

Subtract $4$ from $5$ .

$\frac{y}{3} = 2 x + 1$

Step 1.3

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (2 x + 1)$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $3$ .

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Step 1.4.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 (2 x + 1)$

Step 1.4.1.1.2

Rewrite the expression.

$y = 3 (2 x + 1)$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $3 (2 x + 1)$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = 3 (2 x) + 3 \cdot 1$

Step 1.4.2.1.2

Multiply.

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Step 1.4.2.1.2.1

Multiply $2$ by $3$ .

$y = 6 x + 3 \cdot 1$

Step 1.4.2.1.2.2

Multiply $3$ by $1$ .

$y = 6 x + 3$

Step 2

Using the slope-intercept form, the slope is $6$ .

$m = 6$

Step 3