Algebra Examples

$8 x - \frac{1}{3} y = 16$

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 $x$ .

$8 x - \frac{1}{3} \cdot 0 = 16$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $8 x - \frac{1}{3} \cdot 0$ .

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Step 1.2.1.1

Multiply $- \frac{1}{3} \cdot 0$ .

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Step 1.2.1.1.1

Multiply $0$ by $- 1$ .

$8 x + 0 (\frac{1}{3}) = 16$

Step 1.2.1.1.2

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

$8 x + 0 = 16$

Step 1.2.1.2

Add $8 x$ and $0$ .

$8 x = 16$

Step 1.2.2

Divide each term in $8 x = 16$ by $8$ and simplify.

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Step 1.2.2.1

Divide each term in $8 x = 16$ by $8$ .

$\frac{8 x}{8} = \frac{16}{8}$

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.

$\frac{8 x}{8} = \frac{16}{8}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{8}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $16$ by $8$ .

$x = 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

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 $y$ .

$8 (0) - \frac{1}{3} y = 16$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $8 (0) - \frac{1}{3} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $8$ by $0$ .

$0 - \frac{1}{3} y = 16$

Step 2.2.1.1.2

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

$0 - \frac{y}{3} = 16$

Step 2.2.1.2

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

$- \frac{y}{3} = 16$

Step 2.2.2

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{y}{3}) = - 3 \cdot 16$

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

Simplify $- 3 (- \frac{y}{3})$ .

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Step 2.2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 3 \frac{- y}{3} = - 3 \cdot 16$

Step 2.2.3.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 \cdot 16$

Step 2.2.3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- y}{3} = - 3 \cdot 16$

Step 2.2.3.1.1.1.4

Rewrite the expression.

$- - y = - 3 \cdot 16$

Step 2.2.3.1.1.2

Multiply.

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Step 2.2.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 \cdot 16$

Step 2.2.3.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 \cdot 16$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Multiply $- 3$ by $16$ .

$y = - 48$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 48)$

Step 3

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - 48)$

Step 4