Find the x and y Intercepts y=1/4x+3

$y = \frac{1}{4} x + 3$

Find the x-intercepts.

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

$0 = \frac{1}{4} x + 3$

Solve the equation.

Rewrite the equation as $\frac{1}{4} x + 3 = 0$ .

$\frac{1}{4} x + 3 = 0$

Combine $\frac{1}{4}$ and $x$ .

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

Subtract $3$ from both sides of the equation.

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

Multiply both sides of the equation by $4$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 4 \cdot - 3$

Simplify the right side.

Multiply $4$ by $- 3$ .

$x = - 12$

x-intercept(s) in point form.

x-intercept(s): $(- 12, 0)$

Find the y-intercepts.

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

$y = \frac{1}{4} \cdot (0) + 3$

Solve the equation.

Multiply $\frac{1}{4}$ by $0$ .

$y = \frac{1}{4} \cdot 0 + 3$

Remove parentheses.

$y = \frac{1}{4} \cdot (0) + 3$

Simplify $\frac{1}{4} \cdot (0) + 3$ .

Multiply $\frac{1}{4}$ by $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(- 12, 0)$

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