Find the x and y Intercepts f(x)=(x-3)/(2x+7)

$f (x) = \frac{x - 3}{2 x + 7}$

Find the x-intercepts.

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

$0 = \frac{x - 3}{2 x + 7}$

Solve the equation.

Set the numerator equal to zero.

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

Find the y-intercepts.

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

$y = \frac{(0) - 3}{2 (0) + 7}$

Solve the equation.

Remove parentheses.

$y = \frac{0 - 3}{2 (0) + 7}$

Remove parentheses.

$y = \frac{(0) - 3}{2 (0) + 7}$

Simplify $\frac{(0) - 3}{2 (0) + 7}$ .

Subtract $3$ from $0$ .

$y = \frac{- 3}{2 (0) + 7}$

Simplify the denominator.

Multiply $2$ by $0$ .

$y = \frac{- 3}{0 + 7}$

Add $0$ and $7$ .

$y = \frac{- 3}{7}$

Move the negative in front of the fraction.

$y = - \frac{3}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{7})$

List the intersections.

x-intercept(s): $(3, 0)$

y-intercept(s): $(0, - \frac{3}{7})$