Pre-Algebra Examples

$y - 6 = \frac{5}{6} \cdot (x - 6)$

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 $\frac{5}{6} \cdot (x - 6)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 6 = \frac{5}{6} x + \frac{5}{6} \cdot - 6$

Step 1.2.1.2

Combine $\frac{5}{6}$ and $x$ .

$y - 6 = \frac{5 x}{6} + \frac{5}{6} \cdot - 6$

Step 1.2.1.3

Cancel the common factor of $6$ .

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Step 1.2.1.3.1

Factor $6$ out of $- 6$ .

$y - 6 = \frac{5 x}{6} + \frac{5}{6} \cdot (6 (- 1))$

Step 1.2.1.3.2

Cancel the common factor.

$y - 6 = \frac{5 x}{6} + \frac{5}{6} \cdot (6 \cdot - 1)$

Step 1.2.1.3.3

Rewrite the expression.

$y - 6 = \frac{5 x}{6} + 5 \cdot - 1$

Step 1.2.1.4

Multiply $5$ by $- 1$ .

$y - 6 = \frac{5 x}{6} - 5$

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 $6$ to both sides of the equation.

$y = \frac{5 x}{6} - 5 + 6$

Step 1.3.2

Add $- 5$ and $6$ .

$y = \frac{5 x}{6} + 1$

Step 1.4

Reorder terms.

$y = \frac{5}{6} x + 1$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{5}{6}$

$b = 1$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{5}{6}$

y-intercept: $(0, 1)$

Slope: $\frac{5}{6}$

y-intercept: $(0, 1)$

Step 3