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

$f (x) = 2 x + 3$

Step 1

Find the x-intercepts.

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

$0 = 2 x + 3$

Solve the equation.

Rewrite the equation as $2 x + 3 = 0$ .

$2 x + 3 = 0$

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3}{2}, 0)$

Step 2

Find the y-intercepts.

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

$y = 2 (0) + 3$

Solve the equation.

Remove parentheses.

$y = 2 (0) + 3$

Simplify $2 (0) + 3$ .

Multiply $2$ by $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- \frac{3}{2}, 0)$

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

Step 4