Find the x and y Intercepts f(x)=-2/(3(x-5))+4

$f (x) = - \frac{2}{3 (x - 5)} + 4$

Find the x-intercepts.

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

$0 = - \frac{2}{3 (x - 5)} + 4$

Solve the equation.

Rewrite the equation as $- \frac{2}{3 (x - 5)} + 4 = 0$ .

$- \frac{2}{3 (x - 5)} + 4 = 0$

Subtract $4$ from both sides of the equation.

$- \frac{2}{3 (x - 5)} = - 4$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 (x - 5), 1$

The LCM of one and any expression is the expression.

$3 (x - 5)$

Multiply each term in $- \frac{2}{3 (x - 5)} = - 4$ by $3 (x - 5)$ to eliminate the fractions.

Multiply each term in $- \frac{2}{3 (x - 5)} = - 4$ by $3 (x - 5)$ .

$- \frac{2}{3 (x - 5)} (3 (x - 5)) = - 4 (3 (x - 5))$

Simplify the left side.

Cancel the common factor of $3 (x - 5)$ .

Move the leading negative in $- \frac{2}{3 (x - 5)}$ into the numerator.

$\frac{- 2}{3 (x - 5)} (3 (x - 5)) = - 4 (3 (x - 5))$

Cancel the common factor.

$\frac{- 2}{3 (x - 5)} (3 (x - 5)) = - 4 (3 (x - 5))$

Rewrite the expression.

$- 2 = - 4 (3 (x - 5))$

Simplify the right side.

Apply the distributive property.

$- 2 = - 4 (3 x + 3 \cdot - 5)$

Multiply $3$ by $- 5$ .

$- 2 = - 4 (3 x - 15)$

Apply the distributive property.

$- 2 = - 4 (3 x) - 4 \cdot - 15$

Multiply.

Multiply $3$ by $- 4$ .

$- 2 = - 12 x - 4 \cdot - 15$

Multiply $- 4$ by $- 15$ .

$- 2 = - 12 x + 60$

Solve the equation.

Rewrite the equation as $- 12 x + 60 = - 2$ .

$- 12 x + 60 = - 2$

Move all terms not containing $x$ to the right side of the equation.

Subtract $60$ from both sides of the equation.

$- 12 x = - 2 - 60$

Subtract $60$ from $- 2$ .

$- 12 x = - 62$

Divide each term in $- 12 x = - 62$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 62$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 62}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 62}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 62}{- 12}$

Simplify the right side.

Cancel the common factor of $- 62$ and $- 12$ .

Factor $- 2$ out of $- 62$ .

$x = \frac{- 2 (31)}{- 12}$

Cancel the common factors.

Factor $- 2$ out of $- 12$ .

$x = \frac{- 2 \cdot 31}{- 2 \cdot 6}$

Cancel the common factor.

$x = \frac{- 2 \cdot 31}{- 2 \cdot 6}$

Rewrite the expression.

$x = \frac{31}{6}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{31}{6}, 0)$

Find the y-intercepts.

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

$y = - \frac{2}{3 ((0) - 5)} + 4$

Solve the equation.

Remove parentheses.

$y = - \frac{2}{3 (0 - 5)} + 4$

Remove parentheses.

$y = - \frac{2}{3 ((0) - 5)} + 4$

Simplify $- \frac{2}{3 ((0) - 5)} + 4$ .

Simplify each term.

Subtract $5$ from $0$ .

$y = - \frac{2}{3 \cdot - 5} + 4$

Multiply $3$ by $- 5$ .

$y = - \frac{2}{- 15} + 4$

Move the negative in front of the fraction.

$y = - - \frac{2}{15} + 4$

Multiply $- - \frac{2}{15}$ .

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{2}{15}) + 4$

Multiply $\frac{2}{15}$ by $1$ .

$y = \frac{2}{15} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$y = \frac{2}{15} + 4 \cdot \frac{15}{15}$

Combine $4$ and $\frac{15}{15}$ .

$y = \frac{2}{15} + \frac{4 \cdot 15}{15}$

Combine the numerators over the common denominator.

$y = \frac{2 + 4 \cdot 15}{15}$

Simplify the numerator.

Multiply $4$ by $15$ .

$y = \frac{2 + 60}{15}$

Add $2$ and $60$ .

$y = \frac{62}{15}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{62}{15})$

List the intersections.

x-intercept(s): $(\frac{31}{6}, 0)$

y-intercept(s): $(0, \frac{62}{15})$

Find the x and y Intercepts f(x)=-2/(3(x-5))+4

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