Find the x and y Intercepts y=(18-3x)/(x^2-9x+18)

$y = \frac{18 - 3 x}{x^{2} - 9 x + 18}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{18 - 3 x}{x^{2} - 9 x + 18}$

Solve the equation.

Set the numerator equal to zero.

$18 - 3 x = 0$

Solve the equation for $x$ .

Subtract $18$ from both sides of the equation.

$- 3 x = - 18$

Divide each term in $- 3 x = - 18$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 18$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 3}$

Simplify the right side.

Divide $- 18$ by $- 3$ .

$x = 6$

Exclude the solutions that do not make $0 = \frac{18 - 3 x}{x^{2} - 9 x + 18}$ true.

$No solution$

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{18 - 3 \cdot 0}{{(0)}^{2} - 9 \cdot 0 + 18}$

Solve the equation.

Remove parentheses.

$y = \frac{18 - 3 \cdot 0}{0^{2} - 9 \cdot 0 + 18}$

Remove parentheses.

$y = \frac{18 - 3 \cdot 0}{{(0)}^{2} - 9 \cdot 0 + 18}$

Simplify $\frac{18 - 3 \cdot 0}{{(0)}^{2} - 9 \cdot 0 + 18}$ .

Simplify the numerator.

Multiply $- 3$ by $0$ .

$y = \frac{18 + 0}{0^{2} - 9 \cdot 0 + 18}$

Add $18$ and $0$ .

$y = \frac{18}{0^{2} - 9 \cdot 0 + 18}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{18}{0 - 9 \cdot 0 + 18}$

Multiply $- 9$ by $0$ .

$y = \frac{18}{0 + 0 + 18}$

Add $0$ and $0$ .

$y = \frac{18}{0 + 18}$

Add $0$ and $18$ .

$y = \frac{18}{18}$

Divide $18$ by $18$ .

$y = 1$

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 1)$

Step 4

Find the x and y Intercepts y=(18-3x)/(x^2-9x+18)

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