Precalculus Examples

$y - 4 = \frac{5}{2} (x - 2)$

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

Simplify $\frac{5}{2} (x - 2)$ .

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Step 1.2.1.1

Apply the distributive property.

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

Step 1.2.1.2

Combine $\frac{5}{2}$ and $x$ .

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

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Factor $2$ out of $- 2$ .

$y - 4 = \frac{5 x}{2} + \frac{5}{2} \cdot (2 (- 1))$

Step 1.2.1.3.2

Cancel the common factor.

$y - 4 = \frac{5 x}{2} + \frac{5}{2} \cdot (2 \cdot - 1)$

Step 1.2.1.3.3

Rewrite the expression.

$y - 4 = \frac{5 x}{2} + 5 \cdot - 1$

Step 1.2.1.4

Multiply $5$ by $- 1$ .

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

Step 1.3

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

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Step 1.3.1

Add $4$ to both sides of the equation.

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

Step 1.3.2

Add $- 5$ and $4$ .

$y = \frac{5 x}{2} - 1$

Step 1.4

Reorder terms.

$y = \frac{5}{2} x - 1$

Step 2

Using the slope-intercept form, the slope is $\frac{5}{2}$ .

$m = \frac{5}{2}$

Step 3