Find the x and y Intercepts x^2-9x-24y+20=0

$x^{2} - 9 x - 24 y + 20 = 0$

Find the x-intercepts.

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

$x^{2} - 9 x - 24 \cdot 0 + 20 = 0$

Solve the equation.

Simplify $x^{2} - 9 x - 24 \cdot 0 + 20$ .

Multiply $- 24$ by $0$ .

$x^{2} - 9 x + 0 + 20 = 0$

Add $x^{2} - 9 x$ and $0$ .

$x^{2} - 9 x + 20 = 0$

Factor $x^{2} - 9 x + 20$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $20$ and whose sum is $- 9$ .

$- 5, - 4$

Write the factored form using these integers.

$(x - 5) (x - 4) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x - 4 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The final solution is all the values that make $(x - 5) (x - 4) = 0$ true.

$x = 5, 4$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (4, 0)$

Find the y-intercepts.

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

${(0)}^{2} - 9 \cdot 0 - 24 y + 20 = 0$

Solve the equation.

Simplify ${(0)}^{2} - 9 \cdot 0 - 24 y + 20$ .

Simplify each term.

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

$0 - 9 \cdot 0 - 24 y + 20 = 0$

Multiply $- 9$ by $0$ .

$0 + 0 - 24 y + 20 = 0$

Combine the opposite terms in $0 + 0 - 24 y + 20$ .

Add $0$ and $0$ .

$0 - 24 y + 20 = 0$

Subtract $24 y$ from $0$ .

$- 24 y + 20 = 0$

Subtract $20$ from both sides of the equation.

$- 24 y = - 20$

Divide each term in $- 24 y = - 20$ by $- 24$ and simplify.

Divide each term in $- 24 y = - 20$ by $- 24$ .

$\frac{- 24 y}{- 24} = \frac{- 20}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 y}{- 24} = \frac{- 20}{- 24}$

Divide $y$ by $1$ .

$y = \frac{- 20}{- 24}$

Simplify the right side.

Cancel the common factor of $- 20$ and $- 24$ .

Factor $- 4$ out of $- 20$ .

$y = \frac{- 4 (5)}{- 24}$

Cancel the common factors.

Factor $- 4$ out of $- 24$ .

$y = \frac{- 4 \cdot 5}{- 4 \cdot 6}$

Cancel the common factor.

$y = \frac{- 4 \cdot 5}{- 4 \cdot 6}$

Rewrite the expression.

$y = \frac{5}{6}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{5}{6})$

List the intersections.

x-intercept(s): $(5, 0), (4, 0)$

y-intercept(s): $(0, \frac{5}{6})$

Find the x and y Intercepts x^2-9x-24y+20=0

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