Pre-Algebra Examples

$5 (y + 3) = 6 (y - 5)$

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

Simplify $5 (y + 3)$ .

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Step 1.2.1.1

Apply the distributive property.

$5 y + 5 \cdot 3 = 6 (y - 5)$

Step 1.2.1.2

Multiply $5$ by $3$ .

$5 y + 15 = 6 (y - 5)$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $6 (y - 5)$ .

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Step 1.3.1.1

Apply the distributive property.

$5 y + 15 = 6 y + 6 \cdot - 5$

Step 1.3.1.2

Multiply $6$ by $- 5$ .

$5 y + 15 = 6 y - 30$

Step 1.4

Move all terms containing $y$ to the left side of the equation.

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Step 1.4.1

Subtract $6 y$ from both sides of the equation.

$5 y + 15 - 6 y = - 30$

Step 1.4.2

Subtract $6 y$ from $5 y$ .

$- y + 15 = - 30$

Step 1.5

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

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Step 1.5.1

Subtract $15$ from both sides of the equation.

$- y = - 30 - 15$

Step 1.5.2

Subtract $15$ from $- 30$ .

$- y = - 45$

Step 1.6

Divide each term in $- y = - 45$ by $- 1$ and simplify.

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Step 1.6.1

Divide each term in $- y = - 45$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 45}{- 1}$

Step 1.6.2

Simplify the left side.

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Step 1.6.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 45}{- 1}$

Step 1.6.2.2

Divide $y$ by $1$ .

$y = \frac{- 45}{- 1}$

Step 1.6.3

Simplify the right side.

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Step 1.6.3.1

Divide $- 45$ by $- 1$ .

$y = 45$

Step 2

Using the slope-intercept form, the y-intercept is $45$ .

$b = 45$

Step 3

y-intercept in point form.

$(0, 45)$

Step 4