Precalculus Examples

$6 x + 2 y = 12$

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 $x$ .

$6 x + 2 (0) = 12$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $6 x + 2 (0)$ .

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Step 1.2.1.1

Multiply $2$ by $0$ .

$6 x + 0 = 12$

Step 1.2.1.2

Add $6 x$ and $0$ .

$6 x = 12$

Step 1.2.2

Divide each term in $6 x = 12$ by $6$ and simplify.

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Step 1.2.2.1

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $12$ by $6$ .

$x = 2$

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 $y$ .

$6 (0) + 2 y = 12$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $6 (0) + 2 y$ .

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Step 2.2.1.1

Multiply $6$ by $0$ .

$0 + 2 y = 12$

Step 2.2.1.2

Add $0$ and $2 y$ .

$2 y = 12$

Step 2.2.2

Divide each term in $2 y = 12$ by $2$ and simplify.

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Step 2.2.2.1

Divide each term in $2 y = 12$ by $2$ .

$\frac{2 y}{2} = \frac{12}{2}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{12}{2}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{2}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $12$ by $2$ .

$y = 6$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 6)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 6)$

Step 4