Precalculus Examples

$- 2 x + 3 y = - 6$

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 $x$ .

$- 2 x + 3 (0) = - 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $- 2 x + 3 (0)$ .

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Step 1.2.1.1

Multiply $3$ by $0$ .

$- 2 x + 0 = - 6$

Step 1.2.1.2

Add $- 2 x$ and $0$ .

$- 2 x = - 6$

Step 1.2.2

Divide each term in $- 2 x = - 6$ by $- 2$ and simplify.

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Step 1.2.2.1

Divide each term in $- 2 x = - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 2}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $- 6$ by $- 2$ .

$x = 3$

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 $y$ .

$- 2 \cdot 0 + 3 y = - 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- 2 \cdot 0 + 3 y$ .

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Step 2.2.1.1

Multiply $- 2$ by $0$ .

$0 + 3 y = - 6$

Step 2.2.1.2

Add $0$ and $3 y$ .

$3 y = - 6$

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): $(3, 0)$

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

Step 4