Algebra Examples

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

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 $x$ .

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

Step 1.2

Solve the equation.

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Step 1.2.1

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

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

Step 1.2.2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} x) = 3 \cdot 0$

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 $3 (\frac{1}{3} x)$ .

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Step 1.2.3.1.1.1

Combine $\frac{1}{3}$ and $x$ .

$3 \frac{x}{3} = 3 \cdot 0$

Step 1.2.3.1.1.2

Cancel the common factor of $3$ .

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Step 1.2.3.1.1.2.1

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot 0$

Step 1.2.3.1.1.2.2

Rewrite the expression.

$x = 3 \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $3$ by $0$ .

$x = 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0)$

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $\frac{1}{3}$ by $0$ .

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

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

Multiply $\frac{1}{3}$ by $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0)$

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

Step 4