Finite Math Examples

$- 2 x + \frac{4}{3} y = - 4$

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 $x$ .

$- 2 x + \frac{4}{3} \cdot (0) = - 4$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $- 2 x + \frac{4}{3} \cdot (0)$ .

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Step 1.2.1.1

Multiply $\frac{4}{3}$ by $0$ .

$- 2 x + 0 = - 4$

Step 1.2.1.2

Add $- 2 x$ and $0$ .

$- 2 x = - 4$

Step 1.2.2

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

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Step 1.2.2.1

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $- 4$ by $- 2$ .

$x = 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

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 $y$ .

$- 2 \cdot 0 + \frac{4}{3} y = - 4$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- 2 \cdot 0 + \frac{4}{3} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $- 2$ by $0$ .

$0 + \frac{4}{3} y = - 4$

Step 2.2.1.1.2

Combine $\frac{4}{3}$ and $y$ .

$0 + \frac{4 y}{3} = - 4$

Step 2.2.1.2

Add $0$ and $\frac{4 y}{3}$ .

$\frac{4 y}{3} = - 4$

Step 2.2.2

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 y}{3} = \frac{3}{4} \cdot - 4$

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

Simplify $\frac{3}{4} \cdot \frac{4 y}{3}$ .

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Step 2.2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 y}{3} = \frac{3}{4} \cdot - 4$

Step 2.2.3.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{3}{4} \cdot - 4$

Step 2.2.3.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.3.1.1.2.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{3}{4} \cdot - 4$

Step 2.2.3.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{3}{4} \cdot - 4$

Step 2.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{4} \cdot - 4$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Simplify $\frac{3}{4} \cdot - 4$ .

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Step 2.2.3.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.3.2.1.1.1

Factor $4$ out of $- 4$ .

$y = \frac{3}{4} \cdot (4 (- 1))$

Step 2.2.3.2.1.1.2

Cancel the common factor.

$y = \frac{3}{4} \cdot (4 \cdot - 1)$

Step 2.2.3.2.1.1.3

Rewrite the expression.

$y = 3 \cdot - 1$

Step 2.2.3.2.1.2

Multiply $3$ by $- 1$ .

$y = - 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - 3)$

Step 4