Question

find the x-intercept and y-intercept of the graph of the equation $y = \frac{1}{4}x - 3$.
x-intercept:

y-intercept:

Explanation:

Step1: Find x-intercept (set y=0)

To find the x - intercept, we set \( y = 0 \) in the equation \( y=\frac{1}{4}x - 3 \). So we have the equation \( 0=\frac{1}{4}x-3 \).
First, add 3 to both sides of the equation: \( 0 + 3=\frac{1}{4}x-3 + 3 \), which simplifies to \( 3=\frac{1}{4}x \).
Then, multiply both sides by 4 to solve for x: \( 3\times4=\frac{1}{4}x\times4 \), so \( x = 12 \).

Step2: Find y-intercept (set x=0)

To find the y - intercept, we set \( x = 0 \) in the equation \( y=\frac{1}{4}x-3 \). Substitute \( x = 0 \) into the equation: \( y=\frac{1}{4}(0)-3 \).
Simplify the right - hand side: \( y=0 - 3=-3 \).

Answer:

x - intercept: \( 12 \)
y - intercept: \( - 3 \)