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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $\frac{3 x}{4} + 3 = 0$ .

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

Subtract $3$ from both sides of the equation.

$\frac{3 x}{4} = - 3$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot - 3$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3$

Rewrite the expression.

$x = \frac{4}{3} \cdot - 3$

Simplify the right side.

Simplify $\frac{4}{3} \cdot - 3$ .

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x = \frac{4}{3} \cdot (3 (- 1))$

Cancel the common factor.

$x = \frac{4}{3} \cdot (3 \cdot - 1)$

Rewrite the expression.

$x = 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$x = - 4$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Multiply $3$ by $0$ .

$y = \frac{0}{4} + 3$

Divide $0$ by $4$ .

$y = 0 + 3$

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): $(- 4, 0)$

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

Step 4

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

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