Finite Math Examples

$600 - 5 x + 7.5 y = 100$

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 $x$ .

$600 - 5 x + 7.5 (0) = 100$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $600 - 5 x + 7.5 (0)$ .

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Step 1.2.1.1

Multiply $7.5$ by $0$ .

$600 - 5 x + 0 = 100$

Step 1.2.1.2

Add $600 - 5 x$ and $0$ .

$600 - 5 x = 100$

Step 1.2.2

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

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Step 1.2.2.1

Subtract $600$ from both sides of the equation.

$- 5 x = 100 - 600$

Step 1.2.2.2

Subtract $600$ from $100$ .

$- 5 x = - 500$

Step 1.2.3

Divide each term in $- 5 x = - 500$ by $- 5$ and simplify.

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Step 1.2.3.1

Divide each term in $- 5 x = - 500$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 500}{- 5}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 500}{- 5}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 500}{- 5}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 500$ by $- 5$ .

$x = 100$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(100, 0)$

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 $y$ .

$600 - 5 \cdot 0 + 7.5 y = 100$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $600 - 5 \cdot 0 + 7.5 y$ .

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Step 2.2.1.1

Multiply $- 5$ by $0$ .

$600 + 0 + 7.5 y = 100$

Step 2.2.1.2

Add $600$ and $0$ .

$600 + 7.5 y = 100$

Step 2.2.2

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

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Step 2.2.2.1

Subtract $600$ from both sides of the equation.

$7.5 y = 100 - 600$

Step 2.2.2.2

Subtract $600$ from $100$ .

$7.5 y = - 500$

Step 2.2.3

Divide each term in $7.5 y = - 500$ by $7.5$ and simplify.

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Step 2.2.3.1

Divide each term in $7.5 y = - 500$ by $7.5$ .

$\frac{7.5 y}{7.5} = \frac{- 500}{7.5}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

Cancel the common factor of $7.5$ .

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Step 2.2.3.2.1.1

Cancel the common factor.

$\frac{7.5 y}{7.5} = \frac{- 500}{7.5}$

Step 2.2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 500}{7.5}$

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Divide $- 500$ by $7.5$ .

$y = - 66.\overline{6}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 66.\overline{6})$

Step 3

List the intersections.

x-intercept(s): $(100, 0)$

y-intercept(s): $(0, - 66.\overline{6})$

Step 4