Finite Math Examples

$y = - \frac{5}{9} x + 5$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - \frac{5}{9} x + 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- \frac{5}{9} x + 5 = 0$ .

$- \frac{5}{9} x + 5 = 0$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Combine $x$ and $\frac{5}{9}$ .

$- \frac{x \cdot 5}{9} + 5 = 0$

Step 1.2.2.2

Move $5$ to the left of $x$ .

$- \frac{5 x}{9} + 5 = 0$

Step 1.2.3

Subtract $5$ from both sides of the equation.

$- \frac{5 x}{9} = - 5$

Step 1.2.4

Multiply both sides of the equation by $- \frac{9}{5}$ .

$- \frac{9}{5} (- \frac{5 x}{9}) = - \frac{9}{5} \cdot - 5$

Step 1.2.5

Simplify both sides of the equation.

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Step 1.2.5.1

Simplify the left side.

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Step 1.2.5.1.1

Simplify $- \frac{9}{5} (- \frac{5 x}{9})$ .

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Step 1.2.5.1.1.1

Cancel the common factor of $9$ .

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Step 1.2.5.1.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} (- \frac{5 x}{9}) = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.1.2

Move the leading negative in $- \frac{5 x}{9}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.2

Cancel the common factor of $5$ .

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Step 1.2.5.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.3

Multiply.

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Step 1.2.5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{5} \cdot - 5$

Step 1.2.5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{9}{5} \cdot - 5$

Step 1.2.5.2

Simplify the right side.

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Step 1.2.5.2.1

Simplify $- \frac{9}{5} \cdot - 5$ .

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Step 1.2.5.2.1.1

Cancel the common factor of $5$ .

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Step 1.2.5.2.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$x = \frac{- 9}{5} \cdot - 5$

Step 1.2.5.2.1.1.2

Factor $5$ out of $- 5$ .

$x = \frac{- 9}{5} \cdot (5 (- 1))$

Step 1.2.5.2.1.1.3

Cancel the common factor.

$x = \frac{- 9}{5} \cdot (5 \cdot - 1)$

Step 1.2.5.2.1.1.4

Rewrite the expression.

$x = - 9 \cdot - 1$

Step 1.2.5.2.1.2

Multiply $- 9$ by $- 1$ .

$x = 9$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(9, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - \frac{5}{9} \cdot 0 + 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - \frac{5}{9} \cdot 0 + 5$

Step 2.2.2

Simplify $- \frac{5}{9} \cdot 0 + 5$ .

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Step 2.2.2.1

Multiply $- \frac{5}{9} \cdot 0$ .

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Step 2.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{5}{9}) + 5$

Step 2.2.2.1.2

Multiply $0$ by $\frac{5}{9}$ .

$y = 0 + 5$

Step 2.2.2.2

Add $0$ and $5$ .

$y = 5$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

x-intercept(s): $(9, 0)$

y-intercept(s): $(0, 5)$

Step 4