Finite Math Examples

$8 x = 5 y + 9$

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 $x$ .

$8 x = 5 (0) + 9$

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 $5$ by $0$ .

$8 x = 0 + 9$

Step 1.2.1.2

Add $0$ and $9$ .

$8 x = 9$

Step 1.2.2

Divide each term in $8 x = 9$ by $8$ and simplify.

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Step 1.2.2.1

Divide each term in $8 x = 9$ by $8$ .

$\frac{8 x}{8} = \frac{9}{8}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{9}{8}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{8}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{9}{8}, 0)$

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 $y$ .

$8 (0) = 5 y + 9$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $5 y + 9 = 8 (0)$ .

$5 y + 9 = 8 (0)$

Step 2.2.2

Multiply $8$ by $0$ .

$5 y + 9 = 0$

Step 2.2.3

Subtract $9$ from both sides of the equation.

$5 y = - 9$

Step 2.2.4

Divide each term in $5 y = - 9$ by $5$ and simplify.

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Step 2.2.4.1

Divide each term in $5 y = - 9$ by $5$ .

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

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $5$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

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

Step 2.2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

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): $(\frac{9}{8}, 0)$

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

Step 4