Find the x and y Intercepts y=(24-6x)/(x^2-10x+24)

$y = \frac{24 - 6 x}{x^{2} - 10 x + 24}$

Step 1

Find the x-intercepts.

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

$0 = \frac{24 - 6 x}{x^{2} - 10 x + 24}$

Solve the equation.

Set the numerator equal to zero.

$24 - 6 x = 0$

Solve the equation for $x$ .

Subtract $24$ from both sides of the equation.

$- 6 x = - 24$

Divide each term in $- 6 x = - 24$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 24$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 6}$

Simplify the right side.

Divide $- 24$ by $- 6$ .

$x = 4$

Exclude the solutions that do not make $0 = \frac{24 - 6 x}{x^{2} - 10 x + 24}$ 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 $y$ .

$y = \frac{24 - 6 \cdot 0}{{(0)}^{2} - 10 \cdot 0 + 24}$

Solve the equation.

Remove parentheses.

$y = \frac{24 - 6 \cdot 0}{0^{2} - 10 \cdot 0 + 24}$

Remove parentheses.

$y = \frac{24 - 6 \cdot 0}{{(0)}^{2} - 10 \cdot 0 + 24}$

Simplify $\frac{24 - 6 \cdot 0}{{(0)}^{2} - 10 \cdot 0 + 24}$ .

Simplify the numerator.

Multiply $- 6$ by $0$ .

$y = \frac{24 + 0}{0^{2} - 10 \cdot 0 + 24}$

Add $24$ and $0$ .

$y = \frac{24}{0^{2} - 10 \cdot 0 + 24}$

Simplify the denominator.

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

$y = \frac{24}{0 - 10 \cdot 0 + 24}$

Multiply $- 10$ by $0$ .

$y = \frac{24}{0 + 0 + 24}$

Add $0$ and $0$ .

$y = \frac{24}{0 + 24}$

Add $0$ and $24$ .

$y = \frac{24}{24}$

Divide $24$ by $24$ .

$y = 1$

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=(24-6x)/(x^2-10x+24)

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