Algebra Examples

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

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 $x$ .

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

Step 1.2

Simplify $x + \frac{1}{3} \cdot (0)$ .

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Step 1.2.1

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

$x + 0 = - 3$

Step 1.2.2

Add $x$ and $0$ .

$x = - 3$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 3, 0)$

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

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

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Step 2.2.1.1

Add $0$ and $\frac{1}{3} y$ .

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

Step 2.2.1.2

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

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

Step 2.2.2

Multiply both sides of the equation by $3$ .

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

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1

Cancel the common factor.

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

Step 2.2.3.1.1.2

Rewrite the expression.

$y = 3 \cdot - 3$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Multiply $3$ by $- 3$ .

$y = - 9$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 9)$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0)$

y-intercept(s): $(0, - 9)$

Step 4