Find the Vertical and Horizontal Intercept(s) q(x)=(x-5)/(2x-1)

$q (x) = \frac{x - 5}{2 x - 1}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x - 5}{2 x - 1}$

Solve the equation.

Set the numerator equal to zero.

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{(0) - 5}{2 (0) - 1}$

Solve the equation.

Remove parentheses.

$y = \frac{0 - 5}{2 (0) - 1}$

Remove parentheses.

$y = \frac{(0) - 5}{2 (0) - 1}$

Simplify $\frac{(0) - 5}{2 (0) - 1}$ .

Subtract $5$ from $0$ .

$y = \frac{- 5}{2 (0) - 1}$

Simplify the denominator.

Multiply $2$ by $0$ .

$y = \frac{- 5}{0 - 1}$

Subtract $1$ from $0$ .

$y = \frac{- 5}{- 1}$

Divide $- 5$ by $- 1$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 5)$

Step 4