Finite Math Examples

$y + 1 = \frac{8}{5} \cdot (x + 5)$

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 $x$ .

$(0) + 1 = \frac{8}{5} \cdot (x + 5)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{8}{5} \cdot (x + 5) = (0) + 1$ .

$\frac{8}{5} \cdot (x + 5) = (0) + 1$

Step 1.2.2

Multiply both sides of the equation by $\frac{5}{8}$ .

$\frac{5}{8} (\frac{8}{5} \cdot (x + 5)) = \frac{5}{8} ((0) + 1)$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $\frac{5}{8} (\frac{8}{5} \cdot (x + 5))$ .

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Step 1.2.3.1.1.1

Apply the distributive property.

$\frac{5}{8} (\frac{8}{5} x + \frac{8}{5} \cdot 5) = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.2

Combine $\frac{8}{5}$ and $x$ .

$\frac{5}{8} (\frac{8 x}{5} + \frac{8}{5} \cdot 5) = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.3

Cancel the common factor of $5$ .

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Step 1.2.3.1.1.3.1

Cancel the common factor.

$\frac{5}{8} (\frac{8 x}{5} + \frac{8}{5} \cdot 5) = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.3.2

Rewrite the expression.

$\frac{5}{8} (\frac{8 x}{5} + 8) = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.4

Apply the distributive property.

$\frac{5}{8} \cdot \frac{8 x}{5} + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.5

Cancel the common factor of $5$ .

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Step 1.2.3.1.1.5.1

Cancel the common factor.

$\frac{5}{8} \cdot \frac{8 x}{5} + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.5.2

Rewrite the expression.

$\frac{1}{8} (8 x) + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.6

Cancel the common factor of $8$ .

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Step 1.2.3.1.1.6.1

Factor $8$ out of $8 x$ .

$\frac{1}{8} (8 (x)) + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.6.2

Cancel the common factor.

$\frac{1}{8} (8 x) + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.6.3

Rewrite the expression.

$x + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.7

Cancel the common factor of $8$ .

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Step 1.2.3.1.1.7.1

Cancel the common factor.

$x + \frac{5}{8} \cdot 8 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.1.1.7.2

Rewrite the expression.

$x + 5 = \frac{5}{8} ((0) + 1)$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Simplify $\frac{5}{8} ((0) + 1)$ .

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Step 1.2.3.2.1.1

Add $0$ and $1$ .

$x + 5 = \frac{5}{8} \cdot 1$

Step 1.2.3.2.1.2

Multiply $\frac{5}{8}$ by $1$ .

$x + 5 = \frac{5}{8}$

Step 1.2.4

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

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Step 1.2.4.1

Subtract $5$ from both sides of the equation.

$x = \frac{5}{8} - 5$

Step 1.2.4.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = \frac{5}{8} - 5 \cdot \frac{8}{8}$

Step 1.2.4.3

Combine $- 5$ and $\frac{8}{8}$ .

$x = \frac{5}{8} + \frac{- 5 \cdot 8}{8}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{5 - 5 \cdot 8}{8}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $- 5$ by $8$ .

$x = \frac{5 - 40}{8}$

Step 1.2.4.5.2

Subtract $40$ from $5$ .

$x = \frac{- 35}{8}$

Step 1.2.4.6

Move the negative in front of the fraction.

$x = - \frac{35}{8}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{35}{8}, 0)$

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 $y$ .

$y + 1 = \frac{8}{5} \cdot ((0) + 5)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $\frac{8}{5} \cdot ((0) + 5)$ .

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Step 2.2.1.1

Add $0$ and $5$ .

$y + 1 = \frac{8}{5} \cdot 5$

Step 2.2.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.2.1

Cancel the common factor.

$y + 1 = \frac{8}{5} \cdot 5$

Step 2.2.1.2.2

Rewrite the expression.

$y + 1 = 8$

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 $1$ from both sides of the equation.

$y = 8 - 1$

Step 2.2.2.2

Subtract $1$ from $8$ .

$y = 7$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{35}{8}, 0)$

y-intercept(s): $(0, 7)$

Step 4