Find the x and y Intercepts f(x)=(-4x+17)/(3x)

$f (x) = \frac{- 4 x + 17}{3 x}$

Step 1

Find the x-intercepts.

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

$0 = \frac{- 4 x + 17}{3 x}$

Solve the equation.

Set the numerator equal to zero.

$- 4 x + 17 = 0$

Solve the equation for $x$ .

Subtract $17$ from both sides of the equation.

$- 4 x = - 17$

Divide each term in $- 4 x = - 17$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 17$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 17}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 17}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 17}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{17}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{17}{4}, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{- 4 \cdot 0 + 17}{3 (0)}$

The equation has an undefined fraction.

Undefined

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(\frac{17}{4}, 0)$

y-intercept(s): $None$

Step 4