Pre-Algebra Examples

$y - (- 7) = (\frac{3}{4}) (x - 2)$

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 left side.

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Step 1.2.1

Multiply $- 1$ by $- 7$ .

$y + 7 = (\frac{3}{4}) (x - 2)$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $(\frac{3}{4}) (x - 2)$ .

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Step 1.3.1.1

Apply the distributive property.

$y + 7 = \frac{3}{4} x + \frac{3}{4} \cdot - 2$

Step 1.3.1.2

Combine $\frac{3}{4}$ and $x$ .

$y + 7 = \frac{3 x}{4} + \frac{3}{4} \cdot - 2$

Step 1.3.1.3

Cancel the common factor of $2$ .

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Step 1.3.1.3.1

Factor $2$ out of $4$ .

$y + 7 = \frac{3 x}{4} + \frac{3}{2 (2)} \cdot - 2$

Step 1.3.1.3.2

Factor $2$ out of $- 2$ .

$y + 7 = \frac{3 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 1.3.1.3.3

Cancel the common factor.

$y + 7 = \frac{3 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 1.3.1.3.4

Rewrite the expression.

$y + 7 = \frac{3 x}{4} + \frac{3}{2} \cdot - 1$

Step 1.3.1.4

Combine $\frac{3}{2}$ and $- 1$ .

$y + 7 = \frac{3 x}{4} + \frac{3 \cdot - 1}{2}$

Step 1.3.1.5

Simplify the expression.

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Step 1.3.1.5.1

Multiply $3$ by $- 1$ .

$y + 7 = \frac{3 x}{4} + \frac{- 3}{2}$

Step 1.3.1.5.2

Move the negative in front of the fraction.

$y + 7 = \frac{3 x}{4} - \frac{3}{2}$

Step 1.4

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

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Step 1.4.1

Subtract $7$ from both sides of the equation.

$y = \frac{3 x}{4} - \frac{3}{2} - 7$

Step 1.4.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3 x}{4} - \frac{3}{2} - 7 \cdot \frac{2}{2}$

Step 1.4.3

Combine $- 7$ and $\frac{2}{2}$ .

$y = \frac{3 x}{4} - \frac{3}{2} + \frac{- 7 \cdot 2}{2}$

Step 1.4.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{4} + \frac{- 3 - 7 \cdot 2}{2}$

Step 1.4.5

Simplify the numerator.

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Step 1.4.5.1

Multiply $- 7$ by $2$ .

$y = \frac{3 x}{4} + \frac{- 3 - 14}{2}$

Step 1.4.5.2

Subtract $14$ from $- 3$ .

$y = \frac{3 x}{4} + \frac{- 17}{2}$

Step 1.4.6

Move the negative in front of the fraction.

$y = \frac{3 x}{4} - \frac{17}{2}$

Step 1.5

Reorder terms.

$y = \frac{3}{4} x - \frac{17}{2}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{17}{2}$ .

$b = - \frac{17}{2}$

Step 3

y-intercept in point form.

$(0, - \frac{17}{2})$

Step 4