Algebra Examples

$11 + \frac{x}{3} = - 2 y + 6$

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 $x$ .

$11 + \frac{x}{3} = - 2 \cdot 0 + 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $- 2 \cdot 0 + 6$ .

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Step 1.2.1.1

Multiply $- 2$ by $0$ .

$11 + \frac{x}{3} = 0 + 6$

Step 1.2.1.2

Add $0$ and $6$ .

$11 + \frac{x}{3} = 6$

Step 1.2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.2.1

Subtract $11$ from both sides of the equation.

$\frac{x}{3} = 6 - 11$

Step 1.2.2.2

Subtract $11$ from $6$ .

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

Step 1.2.3

Multiply both sides of the equation by $3$ .

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

Step 1.2.4

Simplify both sides of the equation.

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Step 1.2.4.1

Simplify the left side.

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Step 1.2.4.1.1

Cancel the common factor of $3$ .

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Step 1.2.4.1.1.1

Cancel the common factor.

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

Step 1.2.4.1.1.2

Rewrite the expression.

$x = 3 \cdot - 5$

Step 1.2.4.2

Simplify the right side.

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Step 1.2.4.2.1

Multiply $3$ by $- 5$ .

$x = - 15$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 15, 0)$

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 $y$ .

$11 + \frac{0}{3} = - 2 y + 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $- 2 y + 6 = 11 + \frac{0}{3}$ .

$- 2 y + 6 = 11 + \frac{0}{3}$

Step 2.2.2

Simplify $11 + \frac{0}{3}$ .

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Step 2.2.2.1

Divide $0$ by $3$ .

$- 2 y + 6 = 11 + 0$

Step 2.2.2.2

Add $11$ and $0$ .

$- 2 y + 6 = 11$

Step 2.2.3

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.3.1

Subtract $6$ from both sides of the equation.

$- 2 y = 11 - 6$

Step 2.2.3.2

Subtract $6$ from $11$ .

$- 2 y = 5$

Step 2.2.4

Divide each term in $- 2 y = 5$ by $- 2$ and simplify.

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Step 2.2.4.1

Divide each term in $- 2 y = 5$ by $- 2$ .

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

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

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

Step 2.2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

Move the negative in front of the fraction.

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{2})$

Step 3

List the intersections.

x-intercept(s): $(- 15, 0)$

y-intercept(s): $(0, - \frac{5}{2})$

Step 4