Finite Math Examples

$y = \frac{2}{3} x - 5$

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 $x$ .

$0 = \frac{2}{3} x - 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{2}{3} x - 5 = 0$ .

$\frac{2}{3} x - 5 = 0$

Step 1.2.2

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

$\frac{2 x}{3} - 5 = 0$

Step 1.2.3

Add $5$ to both sides of the equation.

$\frac{2 x}{3} = 5$

Step 1.2.4

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 5$

Step 1.2.5

Simplify both sides of the equation.

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Step 1.2.5.1

Simplify the left side.

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Step 1.2.5.1.1

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 1.2.5.1.1.1

Cancel the common factor of $3$ .

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Step 1.2.5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 5$

Step 1.2.5.1.1.1.2

Rewrite the expression.

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

Step 1.2.5.1.1.2

Cancel the common factor of $2$ .

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Step 1.2.5.1.1.2.1

Factor $2$ out of $2 x$ .

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

Step 1.2.5.1.1.2.2

Cancel the common factor.

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

Step 1.2.5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{2} \cdot 5$

Step 1.2.5.2

Simplify the right side.

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Step 1.2.5.2.1

Multiply $\frac{3}{2} \cdot 5$ .

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Step 1.2.5.2.1.1

Combine $\frac{3}{2}$ and $5$ .

$x = \frac{3 \cdot 5}{2}$

Step 1.2.5.2.1.2

Multiply $3$ by $5$ .

$x = \frac{15}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{15}{2}, 0)$

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 $y$ .

$y = \frac{2}{3} \cdot (0) - 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $\frac{2}{3}$ by $0$ .

$y = \frac{2}{3} \cdot 0 - 5$

Step 2.2.2

Remove parentheses.

$y = \frac{2}{3} \cdot (0) - 5$

Step 2.2.3

Simplify $\frac{2}{3} \cdot (0) - 5$ .

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Step 2.2.3.1

Multiply $\frac{2}{3}$ by $0$ .

$y = 0 - 5$

Step 2.2.3.2

Subtract $5$ from $0$ .

$y = - 5$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{15}{2}, 0)$

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

Step 4