Finite Math Examples

$7 (y - 3) = 7 (\frac{6}{7} \cdot (x - 3))$

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 $x$ .

$7 ((0) - 3) = 7 (\frac{6}{7} \cdot (x - 3))$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $7 (\frac{6}{7}) \cdot (x - 3) = 7 ((0) - 3)$ .

$7 (\frac{6}{7}) \cdot (x - 3) = 7 ((0) - 3)$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$7 (\frac{6}{7}) \cdot (x - 3) = 7 ((0) - 3)$

Step 1.2.2.1.2

Rewrite the expression.

$6 \cdot (x - 3) = 7 ((0) - 3)$

Step 1.2.2.2

Subtract $3$ from $0$ .

$6 \cdot (x - 3) = 7 \cdot - 3$

Step 1.2.2.3

Multiply $7$ by $- 3$ .

$6 \cdot (x - 3) = - 21$

Step 1.2.3

Divide each term in $6 \cdot (x - 3) = - 21$ by $6$ and simplify.

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Step 1.2.3.1

Divide each term in $6 \cdot (x - 3) = - 21$ by $6$ .

$\frac{6 \cdot (x - 3)}{6} = \frac{- 21}{6}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $6$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{6 \cdot (x - 3)}{6} = \frac{- 21}{6}$

Step 1.2.3.2.1.2

Divide $x - 3$ by $1$ .

$x - 3 = \frac{- 21}{6}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Cancel the common factor of $- 21$ and $6$ .

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Step 1.2.3.3.1.1

Factor $3$ out of $- 21$ .

$x - 3 = \frac{3 (- 7)}{6}$

Step 1.2.3.3.1.2

Cancel the common factors.

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Step 1.2.3.3.1.2.1

Factor $3$ out of $6$ .

$x - 3 = \frac{3 \cdot - 7}{3 \cdot 2}$

Step 1.2.3.3.1.2.2

Cancel the common factor.

$x - 3 = \frac{3 \cdot - 7}{3 \cdot 2}$

Step 1.2.3.3.1.2.3

Rewrite the expression.

$x - 3 = \frac{- 7}{2}$

Step 1.2.3.3.2

Move the negative in front of the fraction.

$x - 3 = - \frac{7}{2}$

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 $3$ to both sides of the equation.

$x = - \frac{7}{2} + 3$

Step 1.2.4.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{7}{2} + 3 \cdot \frac{2}{2}$

Step 1.2.4.3

Combine $3$ and $\frac{2}{2}$ .

$x = - \frac{7}{2} + \frac{3 \cdot 2}{2}$

Step 1.2.4.4

Combine the numerators over the common denominator.

$x = \frac{- 7 + 3 \cdot 2}{2}$

Step 1.2.4.5

Simplify the numerator.

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Step 1.2.4.5.1

Multiply $3$ by $2$ .

$x = \frac{- 7 + 6}{2}$

Step 1.2.4.5.2

Add $- 7$ and $6$ .

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

Step 1.2.4.6

Move the negative in front of the fraction.

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

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 $y$ .

$7 (y - 3) = 7 (\frac{6}{7} \cdot ((0) - 3))$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify.

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Step 2.2.1.1

Subtract $3$ from $0$ .

$7 (y - 3) = 7 (\frac{6}{7} \cdot - 3)$

Step 2.2.1.2

Multiply $\frac{6}{7} \cdot - 3$ .

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Step 2.2.1.2.1

Combine $\frac{6}{7}$ and $- 3$ .

$7 (y - 3) = 7 \frac{6 \cdot - 3}{7}$

Step 2.2.1.2.2

Multiply $6$ by $- 3$ .

$7 (y - 3) = 7 (\frac{- 18}{7})$

Step 2.2.1.3

Cancel the common factor of $7$ .

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Step 2.2.1.3.1

Cancel the common factor.

$7 (y - 3) = 7 (\frac{- 18}{7})$

Step 2.2.1.3.2

Rewrite the expression.

$7 (y - 3) = - 18$

Step 2.2.2

Divide each term in $7 (y - 3) = - 18$ by $7$ and simplify.

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Step 2.2.2.1

Divide each term in $7 (y - 3) = - 18$ by $7$ .

$\frac{7 (y - 3)}{7} = \frac{- 18}{7}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{7 (y - 3)}{7} = \frac{- 18}{7}$

Step 2.2.2.2.1.2

Divide $y - 3$ by $1$ .

$y - 3 = \frac{- 18}{7}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Move the negative in front of the fraction.

$y - 3 = - \frac{18}{7}$

Step 2.2.3

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

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Step 2.2.3.1

Add $3$ to both sides of the equation.

$y = - \frac{18}{7} + 3$

Step 2.2.3.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{18}{7} + 3 \cdot \frac{7}{7}$

Step 2.2.3.3

Combine $3$ and $\frac{7}{7}$ .

$y = - \frac{18}{7} + \frac{3 \cdot 7}{7}$

Step 2.2.3.4

Combine the numerators over the common denominator.

$y = \frac{- 18 + 3 \cdot 7}{7}$

Step 2.2.3.5

Simplify the numerator.

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Step 2.2.3.5.1

Multiply $3$ by $7$ .

$y = \frac{- 18 + 21}{7}$

Step 2.2.3.5.2

Add $- 18$ and $21$ .

$y = \frac{3}{7}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{7})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{3}{7})$

Step 4