Finite Math Examples

$y - 3 = \frac{6}{5} \cdot (x - 4)$

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 $x$ .

$(0) - 3 = \frac{6}{5} \cdot (x - 4)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{6}{5} \cdot (x - 4) = (0) - 3$ .

$\frac{6}{5} \cdot (x - 4) = (0) - 3$

Step 1.2.2

Multiply both sides of the equation by $\frac{5}{6}$ .

$\frac{5}{6} (\frac{6}{5} \cdot (x - 4)) = \frac{5}{6} ((0) - 3)$

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 $\frac{5}{6} (\frac{6}{5} \cdot (x - 4))$ .

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Step 1.2.3.1.1.1

Apply the distributive property.

$\frac{5}{6} (\frac{6}{5} x + \frac{6}{5} \cdot - 4) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.2

Combine $\frac{6}{5}$ and $x$ .

$\frac{5}{6} (\frac{6 x}{5} + \frac{6}{5} \cdot - 4) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.3

Multiply $\frac{6}{5} \cdot - 4$ .

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Step 1.2.3.1.1.3.1

Combine $\frac{6}{5}$ and $- 4$ .

$\frac{5}{6} (\frac{6 x}{5} + \frac{6 \cdot - 4}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.3.2

Multiply $6$ by $- 4$ .

$\frac{5}{6} (\frac{6 x}{5} + \frac{- 24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.4

Move the negative in front of the fraction.

$\frac{5}{6} (\frac{6 x}{5} - \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.5

Apply the distributive property.

$\frac{5}{6} \cdot \frac{6 x}{5} + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.6

Cancel the common factor of $5$ .

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Step 1.2.3.1.1.6.1

Cancel the common factor.

$\frac{5}{6} \cdot \frac{6 x}{5} + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.6.2

Rewrite the expression.

$\frac{1}{6} (6 x) + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.7

Cancel the common factor of $6$ .

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Step 1.2.3.1.1.7.1

Factor $6$ out of $6 x$ .

$\frac{1}{6} (6 (x)) + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.7.2

Cancel the common factor.

$\frac{1}{6} (6 x) + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.7.3

Rewrite the expression.

$x + \frac{5}{6} (- \frac{24}{5}) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.8

Cancel the common factor of $5$ .

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Step 1.2.3.1.1.8.1

Move the leading negative in $- \frac{24}{5}$ into the numerator.

$x + \frac{5}{6} \cdot \frac{- 24}{5} = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.8.2

Cancel the common factor.

$x + \frac{5}{6} \cdot \frac{- 24}{5} = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.8.3

Rewrite the expression.

$x + \frac{1}{6} \cdot - 24 = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.9

Cancel the common factor of $6$ .

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Step 1.2.3.1.1.9.1

Factor $6$ out of $- 24$ .

$x + \frac{1}{6} \cdot (6 (- 4)) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.9.2

Cancel the common factor.

$x + \frac{1}{6} \cdot (6 \cdot - 4) = \frac{5}{6} ((0) - 3)$

Step 1.2.3.1.1.9.3

Rewrite the expression.

$x - 4 = \frac{5}{6} ((0) - 3)$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Simplify $\frac{5}{6} ((0) - 3)$ .

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Step 1.2.3.2.1.1

Subtract $3$ from $0$ .

$x - 4 = \frac{5}{6} \cdot - 3$

Step 1.2.3.2.1.2

Cancel the common factor of $3$ .

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Step 1.2.3.2.1.2.1

Factor $3$ out of $6$ .

$x - 4 = \frac{5}{3 (2)} \cdot - 3$

Step 1.2.3.2.1.2.2

Factor $3$ out of $- 3$ .

$x - 4 = \frac{5}{3 \cdot 2} \cdot (3 \cdot - 1)$

Step 1.2.3.2.1.2.3

Cancel the common factor.

$x - 4 = \frac{5}{3 \cdot 2} \cdot (3 \cdot - 1)$

Step 1.2.3.2.1.2.4

Rewrite the expression.

$x - 4 = \frac{5}{2} \cdot - 1$

Step 1.2.3.2.1.3

Combine $\frac{5}{2}$ and $- 1$ .

$x - 4 = \frac{5 \cdot - 1}{2}$

Step 1.2.3.2.1.4

Simplify the expression.

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Step 1.2.3.2.1.4.1

Multiply $5$ by $- 1$ .

$x - 4 = \frac{- 5}{2}$

Step 1.2.3.2.1.4.2

Move the negative in front of the fraction.

$x - 4 = - \frac{5}{2}$

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

Add $4$ to both sides of the equation.

$x = - \frac{5}{2} + 4$

Step 1.2.4.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{5}{2} + 4 \cdot \frac{2}{2}$

Step 1.2.4.3

Combine $4$ and $\frac{2}{2}$ .

$x = - \frac{5}{2} + \frac{4 \cdot 2}{2}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{- 5 + 4 \cdot 2}{2}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $4$ by $2$ .

$x = \frac{- 5 + 8}{2}$

Step 1.2.4.5.2

Add $- 5$ and $8$ .

$x = \frac{3}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0)$

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 $y$ .

$y - 3 = \frac{6}{5} \cdot ((0) - 4)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $\frac{6}{5} \cdot ((0) - 4)$ .

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Step 2.2.1.1

Subtract $4$ from $0$ .

$y - 3 = \frac{6}{5} \cdot - 4$

Step 2.2.1.2

Multiply $\frac{6}{5} \cdot - 4$ .

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Step 2.2.1.2.1

Combine $\frac{6}{5}$ and $- 4$ .

$y - 3 = \frac{6 \cdot - 4}{5}$

Step 2.2.1.2.2

Multiply $6$ by $- 4$ .

$y - 3 = \frac{- 24}{5}$

Step 2.2.1.3

Move the negative in front of the fraction.

$y - 3 = - \frac{24}{5}$

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

Add $3$ to both sides of the equation.

$y = - \frac{24}{5} + 3$

Step 2.2.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{24}{5} + 3 \cdot \frac{5}{5}$

Step 2.2.2.3

Combine $3$ and $\frac{5}{5}$ .

$y = - \frac{24}{5} + \frac{3 \cdot 5}{5}$

Step 2.2.2.4

Combine the numerators over the common denominator.

$y = \frac{- 24 + 3 \cdot 5}{5}$

Step 2.2.2.5

Simplify the numerator.

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Step 2.2.2.5.1

Multiply $3$ by $5$ .

$y = \frac{- 24 + 15}{5}$

Step 2.2.2.5.2

Add $- 24$ and $15$ .

$y = \frac{- 9}{5}$

Step 2.2.2.6

Move the negative in front of the fraction.

$y = - \frac{9}{5}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{9}{5})$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0)$

y-intercept(s): $(0, - \frac{9}{5})$

Step 4