Question

find the x - and y - intercepts of the graph of 9x + 4y = 18. state each answer as an integer or an improper fraction in simplest form.

Explanation:

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

Substitute \( y = 0 \) into the equation \( 9x + 4y = 18 \).
We get \( 9x + 4(0)=18 \), which simplifies to \( 9x = 18 \).
Divide both sides by 9: \( x=\frac{18}{9}=2 \).

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

Substitute \( x = 0 \) into the equation \( 9x + 4y = 18 \).
We get \( 9(0)+4y = 18 \), which simplifies to \( 4y = 18 \).
Divide both sides by 4: \( y=\frac{18}{4}=\frac{9}{2} \).

Answer:

x - intercept: \( 2 \)
y - intercept: \( \frac{9}{2} \)