Pre-Algebra Examples

$11 x - 7 y + 3 = 4 x - 4 y - 3$

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

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

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Step 1.2.1

Add $4 y$ to both sides of the equation.

$11 x - 7 y + 3 + 4 y = 4 x - 3$

Step 1.2.2

Add $- 7 y$ and $4 y$ .

$11 x - 3 y + 3 = 4 x - 3$

Step 1.3

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

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Step 1.3.1

Subtract $11 x$ from both sides of the equation.

$- 3 y + 3 = 4 x - 3 - 11 x$

Step 1.3.2

Subtract $3$ from both sides of the equation.

$- 3 y = 4 x - 3 - 11 x - 3$

Step 1.3.3

Subtract $11 x$ from $4 x$ .

$- 3 y = - 7 x - 3 - 3$

Step 1.3.4

Subtract $3$ from $- 3$ .

$- 3 y = - 7 x - 6$

Step 1.4

Divide each term in $- 3 y = - 7 x - 6$ by $- 3$ and simplify.

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Step 1.4.1

Divide each term in $- 3 y = - 7 x - 6$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 7 x}{- 3} + \frac{- 6}{- 3}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $- 3$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 7 x}{- 3} + \frac{- 6}{- 3}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7 x}{- 3} + \frac{- 6}{- 3}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{7 x}{3} + \frac{- 6}{- 3}$

Step 1.4.3.1.2

Divide $- 6$ by $- 3$ .

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

Step 1.5

Reorder terms.

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

Step 2

Using the slope-intercept form, the y-intercept is $2$ .

$b = 2$

Step 3

y-intercept in point form.

$(0, 2)$

Step 4