Precalculus Examples

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

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

Combine $\frac{1}{2}$ and $y$ .

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

Step 1.3

Subtract $2 x$ from both sides of the equation.

$\frac{y}{2} = - 3 - 2 x$

Step 1.4

Multiply both sides of the equation by $2$ .

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

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Cancel the common factor of $2$ .

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Step 1.5.1.1.1

Cancel the common factor.

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

Step 1.5.1.1.2

Rewrite the expression.

$y = 2 (- 3 - 2 x)$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $2 (- 3 - 2 x)$ .

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Step 1.5.2.1.1

Apply the distributive property.

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

Step 1.5.2.1.2

Multiply.

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Step 1.5.2.1.2.1

Multiply $2$ by $- 3$ .

$y = - 6 + 2 (- 2 x)$

Step 1.5.2.1.2.2

Multiply $- 2$ by $2$ .

$y = - 6 - 4 x$

Step 1.6

Reorder $- 6$ and $- 4 x$ .

$y = - 4 x - 6$

Step 2

Using the slope-intercept form, the slope is $- 4$ .

$m = - 4$

Step 3