Algebra Examples

$y - 5 = \frac{5}{3} (x - 3)$

Step 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 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the right side.

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Step 2.1.1

Simplify $\frac{5}{3} (x - 3)$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Combine $\frac{5}{3}$ and $x$ .

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

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $- 3$ .

$y - 5 = \frac{5 x}{3} + \frac{5}{3} \cdot (3 (- 1))$

Step 2.1.1.3.2

Cancel the common factor.

$y - 5 = \frac{5 x}{3} + \frac{5}{3} \cdot (3 \cdot - 1)$

Step 2.1.1.3.3

Rewrite the expression.

$y - 5 = \frac{5 x}{3} + 5 \cdot - 1$

Step 2.1.1.4

Multiply $5$ by $- 1$ .

$y - 5 = \frac{5 x}{3} - 5$

Step 2.2

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

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Step 2.2.1

Add $5$ to both sides of the equation.

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

Step 2.2.2

Combine the opposite terms in $\frac{5 x}{3} - 5 + 5$ .

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Step 2.2.2.1

Add $- 5$ and $5$ .

$y = \frac{5 x}{3} + 0$

Step 2.2.2.2

Add $\frac{5 x}{3}$ and $0$ .

$y = \frac{5 x}{3}$

Step 2.3

Reorder terms.

$y = \frac{5}{3} x$