Finite Math Examples

$12 x - 3 y = 15$

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 $x$ .

$12 x - 3 \cdot 0 = 15$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $12 x - 3 \cdot 0$ .

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Step 1.2.1.1

Multiply $- 3$ by $0$ .

$12 x + 0 = 15$

Step 1.2.1.2

Add $12 x$ and $0$ .

$12 x = 15$

Step 1.2.2

Divide each term in $12 x = 15$ by $12$ and simplify.

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Step 1.2.2.1

Divide each term in $12 x = 15$ by $12$ .

$\frac{12 x}{12} = \frac{15}{12}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $12$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{15}{12}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{12}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Cancel the common factor of $15$ and $12$ .

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Step 1.2.2.3.1.1

Factor $3$ out of $15$ .

$x = \frac{3 (5)}{12}$

Step 1.2.2.3.1.2

Cancel the common factors.

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Step 1.2.2.3.1.2.1

Factor $3$ out of $12$ .

$x = \frac{3 \cdot 5}{3 \cdot 4}$

Step 1.2.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 5}{3 \cdot 4}$

Step 1.2.2.3.1.2.3

Rewrite the expression.

$x = \frac{5}{4}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{4}, 0)$

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 $y$ .

$12 (0) - 3 y = 15$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $12 (0) - 3 y$ .

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Step 2.2.1.1

Multiply $12$ by $0$ .

$0 - 3 y = 15$

Step 2.2.1.2

Subtract $3 y$ from $0$ .

$- 3 y = 15$

Step 2.2.2

Divide each term in $- 3 y = 15$ by $- 3$ and simplify.

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Step 2.2.2.1

Divide each term in $- 3 y = 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{15}{- 3}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $15$ by $- 3$ .

$y = - 5$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{5}{4}, 0)$

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

Step 4