Finite Math Examples

$2 x = \frac{5}{4} y + 1$

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 $x$ .

$2 x = \frac{5}{4} \cdot (0) + 1$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify.

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Step 1.2.1.1

Multiply $\frac{5}{4}$ by $0$ .

$2 x = 0 + 1$

Step 1.2.1.2

Add $0$ and $1$ .

$2 x = 1$

Step 1.2.2

Divide each term in $2 x = 1$ by $2$ and simplify.

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Step 1.2.2.1

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

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.

$\frac{2 x}{2} = \frac{1}{2}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{2}, 0)$

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 $y$ .

$2 (0) = \frac{5}{4} y + 1$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $\frac{5}{4} y + 1 = 2 (0)$ .

$\frac{5}{4} y + 1 = 2 (0)$

Step 2.2.2

Combine $\frac{5}{4}$ and $y$ .

$\frac{5 y}{4} + 1 = 2 (0)$

Step 2.2.3

Multiply $2$ by $0$ .

$\frac{5 y}{4} + 1 = 0$

Step 2.2.4

Subtract $1$ from both sides of the equation.

$\frac{5 y}{4} = - 1$

Step 2.2.5

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} \cdot - 1$

Step 2.2.6

Simplify both sides of the equation.

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Step 2.2.6.1

Simplify the left side.

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Step 2.2.6.1.1

Simplify $\frac{4}{5} \cdot \frac{5 y}{4}$ .

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Step 2.2.6.1.1.1

Cancel the common factor of $4$ .

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Step 2.2.6.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} \cdot - 1$

Step 2.2.6.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{4}{5} \cdot - 1$

Step 2.2.6.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.6.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{4}{5} \cdot - 1$

Step 2.2.6.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{4}{5} \cdot - 1$

Step 2.2.6.1.1.2.3

Rewrite the expression.

$y = \frac{4}{5} \cdot - 1$

Step 2.2.6.2

Simplify the right side.

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Step 2.2.6.2.1

Simplify $\frac{4}{5} \cdot - 1$ .

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Step 2.2.6.2.1.1

Multiply $\frac{4}{5} \cdot - 1$ .

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Step 2.2.6.2.1.1.1

Combine $\frac{4}{5}$ and $- 1$ .

$y = \frac{4 \cdot - 1}{5}$

Step 2.2.6.2.1.1.2

Multiply $4$ by $- 1$ .

$y = \frac{- 4}{5}$

Step 2.2.6.2.1.2

Move the negative in front of the fraction.

$y = - \frac{4}{5}$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{2}, 0)$

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

Step 4