Finite Math Examples

$y = 3 x - \frac{1}{3}$

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 $x$ .

$0 = 3 x - \frac{1}{3}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $3 x - \frac{1}{3} = 0$ .

$3 x - \frac{1}{3} = 0$

Step 1.2.2

Add $\frac{1}{3}$ to both sides of the equation.

$3 x = \frac{1}{3}$

Step 1.2.3

Divide each term in $3 x = \frac{1}{3}$ by $3$ and simplify.

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Step 1.2.3.1

Divide each term in $3 x = \frac{1}{3}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{1}{3}}{3}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $3$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{1}{3}}{3}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{3}}{3}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{3} \cdot \frac{1}{3}$

Step 1.2.3.3.2

Multiply $\frac{1}{3} \cdot \frac{1}{3}$ .

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Step 1.2.3.3.2.1

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$x = \frac{1}{3 \cdot 3}$

Step 1.2.3.3.2.2

Multiply $3$ by $3$ .

$x = \frac{1}{9}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{9}, 0)$

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 $y$ .

$y = 3 (0) - \frac{1}{3}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 3 (0) - \frac{1}{3}$

Step 2.2.2

Simplify $3 (0) - \frac{1}{3}$ .

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Step 2.2.2.1

Multiply $3$ by $0$ .

$y = 0 - \frac{1}{3}$

Step 2.2.2.2

Subtract $\frac{1}{3}$ from $0$ .

$y = - \frac{1}{3}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{3})$

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{9}, 0)$

y-intercept(s): $(0, - \frac{1}{3})$

Step 4