Precalculus Examples

$9 y = x + 3$

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 $x$ .

$9 (0) = x + 3$

Step 1.2

Solve the equation.

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Step 1.2.1

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

$x + 3 = 9 (0)$

Step 1.2.2

Multiply $9$ by $0$ .

$x + 3 = 0$

Step 1.2.3

Subtract $3$ from both sides of the equation.

$x = - 3$

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 $y$ .

$9 y = (0) + 3$

Step 2.2

Solve the equation.

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Step 2.2.1

Add $0$ and $3$ .

$9 y = 3$

Step 2.2.2

Divide each term in $9 y = 3$ by $9$ and simplify.

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Step 2.2.2.1

Divide each term in $9 y = 3$ by $9$ .

$\frac{9 y}{9} = \frac{3}{9}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $9$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{3}{9}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{9}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Cancel the common factor of $3$ and $9$ .

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Step 2.2.2.3.1.1

Factor $3$ out of $3$ .

$y = \frac{3 (1)}{9}$

Step 2.2.2.3.1.2

Cancel the common factors.

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Step 2.2.2.3.1.2.1

Factor $3$ out of $9$ .

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

Step 2.2.2.3.1.2.2

Cancel the common factor.

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

Step 2.2.2.3.1.2.3

Rewrite the expression.

$y = \frac{1}{3}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{3})$

Step 3

List the intersections.

x-intercept(s): $(- 3, 0)$

y-intercept(s): $(0, \frac{1}{3})$

Step 4