Finite Math Examples

$y - \frac{1}{4} x - 5 = 0$

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 $x$ .

$(0) - \frac{1}{4} x - 5 = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $(0) - \frac{1}{4} x - 5$ .

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Step 1.2.1.1

Subtract $\frac{1}{4} x$ from $0$ .

$- \frac{1}{4} x - 5 = 0$

Step 1.2.1.2

Combine $x$ and $\frac{1}{4}$ .

$- \frac{x}{4} - 5 = 0$

Step 1.2.2

Add $5$ to both sides of the equation.

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

Step 1.2.3

Multiply both sides of the equation by $- 4$ .

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

Step 1.2.4

Simplify both sides of the equation.

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Step 1.2.4.1

Simplify the left side.

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Step 1.2.4.1.1

Simplify $- 4 (- \frac{x}{4})$ .

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Step 1.2.4.1.1.1

Cancel the common factor of $4$ .

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Step 1.2.4.1.1.1.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

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

Step 1.2.4.1.1.1.2

Factor $4$ out of $- 4$ .

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

Step 1.2.4.1.1.1.3

Cancel the common factor.

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

Step 1.2.4.1.1.1.4

Rewrite the expression.

$- - x = - 4 \cdot 5$

Step 1.2.4.1.1.2

Multiply.

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Step 1.2.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 4 \cdot 5$

Step 1.2.4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 4 \cdot 5$

Step 1.2.4.2

Simplify the right side.

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Step 1.2.4.2.1

Multiply $- 4$ by $5$ .

$x = - 20$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 20, 0)$

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 $y$ .

$y - \frac{1}{4} \cdot 0 - 5 = 0$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $y - \frac{1}{4} \cdot 0 - 5$ .

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Step 2.2.1.1

Multiply $- \frac{1}{4} \cdot 0$ .

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Step 2.2.1.1.1

Multiply $0$ by $- 1$ .

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

Step 2.2.1.1.2

Multiply $0$ by $\frac{1}{4}$ .

$y + 0 - 5 = 0$

Step 2.2.1.2

Add $y$ and $0$ .

$y - 5 = 0$

Step 2.2.2

Add $5$ to both sides of the equation.

$y = 5$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 20, 0)$

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

Step 4