Finite Math Examples

$10 - \frac{1}{3} y = 3 x$

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

Combine $y$ and $\frac{1}{3}$ .

$10 - \frac{y}{3} = 3 x$

Step 1.3

Subtract $10$ from both sides of the equation.

$- \frac{y}{3} = 3 x - 10$

Step 1.4

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{y}{3}) = - 3 (3 x - 10)$

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 1.5.1.1.1

Cancel the common factor of $3$ .

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Step 1.5.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 3 \frac{- y}{3} = - 3 (3 x - 10)$

Step 1.5.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 (3 x - 10)$

Step 1.5.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- y}{3} = - 3 (3 x - 10)$

Step 1.5.1.1.1.4

Rewrite the expression.

$- - y = - 3 (3 x - 10)$

Step 1.5.1.1.2

Multiply.

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Step 1.5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 (3 x - 10)$

Step 1.5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 (3 x - 10)$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $- 3 (3 x - 10)$ .

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Step 1.5.2.1.1

Apply the distributive property.

$y = - 3 (3 x) - 3 \cdot - 10$

Step 1.5.2.1.2

Multiply.

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Step 1.5.2.1.2.1

Multiply $3$ by $- 3$ .

$y = - 9 x - 3 \cdot - 10$

Step 1.5.2.1.2.2

Multiply $- 3$ by $- 10$ .

$y = - 9 x + 30$

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 $y = m x + b$ .

$m = - 9$

$b = 30$

Step 2.2

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

Slope: $- 9$

y-intercept: $(0, 30)$

Slope: $- 9$

y-intercept: $(0, 30)$

Step 3