Newton Robbins
06/03/2024 · Senior High School
Find the x - and y -intercepts of the graph of \( 9 x+3 y=30 \). State each answer as an integer or an improper fraction in simplest form. Answer Attempt 2 out of 2 x-intercept: \( \square \)-intercept: Submit Answer
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Tutor-Verified Answer
Step-by-step Solution
To find the x-intercept and y-intercept of the equation \( 9x + 3y = 30 \), we can follow these steps:
### Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). We can substitute \( y = 0 \) into the equation:
\[
9x + 3(0) = 30
\]
\[
9x = 30
\]
\[
x = \frac{30}{9} = \frac{10}{3}
\]
So, the x-intercept is \( \frac{10}{3} \).
### Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). We can substitute \( x = 0 \) into the equation:
\[
9(0) + 3y = 30
\]
\[
3y = 30
\]
\[
y = \frac{30}{3} = 10
\]
So, the y-intercept is \( 10 \).
### Summary of intercepts:
- x-intercept: \( \frac{10}{3} \)
- y-intercept: \( 10 \)
You can fill in the blanks as follows:
- x-intercept: \( \frac{10}{3} \)
- y-intercept: \( 10 \)
Quick Answer
x-intercept: \( \frac{10}{3} \), y-intercept: 10
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