Algebra Examples

$3 y = 9 x + 6$

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 $x$ .

$3 (0) = 9 x + 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $9 x + 6 = 3 (0)$ .

$9 x + 6 = 3 (0)$

Step 1.2.2

Multiply $3$ by $0$ .

$9 x + 6 = 0$

Step 1.2.3

Subtract $6$ from both sides of the equation.

$9 x = - 6$

Step 1.2.4

Divide each term in $9 x = - 6$ by $9$ and simplify.

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Step 1.2.4.1

Divide each term in $9 x = - 6$ by $9$ .

$\frac{9 x}{9} = \frac{- 6}{9}$

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Cancel the common factor of $9$ .

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Step 1.2.4.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 6}{9}$

Step 1.2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{9}$

Step 1.2.4.3

Simplify the right side.

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Step 1.2.4.3.1

Cancel the common factor of $- 6$ and $9$ .

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Step 1.2.4.3.1.1

Factor $3$ out of $- 6$ .

$x = \frac{3 (- 2)}{9}$

Step 1.2.4.3.1.2

Cancel the common factors.

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Step 1.2.4.3.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3 \cdot - 2}{3 \cdot 3}$

Step 1.2.4.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot - 2}{3 \cdot 3}$

Step 1.2.4.3.1.2.3

Rewrite the expression.

$x = \frac{- 2}{3}$

Step 1.2.4.3.2

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{2}{3}, 0)$

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 $y$ .

$3 y = 9 (0) + 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify.

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Step 2.2.1.1

Multiply $9$ by $0$ .

$3 y = 0 + 6$

Step 2.2.1.2

Add $0$ and $6$ .

$3 y = 6$

Step 2.2.2

Divide each term in $3 y = 6$ by $3$ and simplify.

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Step 2.2.2.1

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{3}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $6$ by $3$ .

$y = 2$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- \frac{2}{3}, 0)$

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

Step 4