https://file.aiquickdraw.com/mathbot/file/17284185648079dd5z4ik.jpg

Let's solve the problem based on the equation shown in the image:

The given linear equation is:

\[
5x - 3y - 45 = 0
\]

### Part 1: Finding the \( x \)-intercept
To find the \( x \)-intercept, we set \( y = 0 \) and solve for \( x \):

\[
5x - 3(0) - 45 = 0
\]
\[
5x - 45 = 0
\]
\[
5x = 45
\]
\[
x = \frac{45}{5} = 9
\]

So, the \( x \)-intercept is at \( (9, 0) \). Hence, \( a = 9 \).

### Part 2: Finding the \( y \)-intercept
To find the \( y \)-intercept, we set \( x = 0 \) and solve for \( y \):

\[
5(0) - 3y - 45 = 0
\]
\[
-3y - 45 = 0
\]
\[
-3y = 45
\]
\[
y = \frac{45}{-3} = -15
\]

So, the \( y \)-intercept is at \( (0, -15) \). Hence, \( b = -15 \).

### Final Answer:
- \( a = 9 \)
- \( b = -15 \)

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you graph this line based on the intercepts?
2. Can you rewrite the equation in slope-intercept form (\( y = mx + b \))?
3. How do you find the slope of this line?
4. What does the slope of this line tell you about the steepness and direction?
5. How would this equation change if you shifted the line up by 5 units?

**Tip:** Always check your intercepts by substituting them back into the original equation to ensure they satisfy it.

Determine the x and y intercepts for the given linear equation: 5x - 3y - 45 = 0.

Learn how to find the x and y intercepts for the linear equation 5x - 3y - 45 = 0 with a detailed solution. This problem focuses on key algebraic concepts such as intercepts and linear equations. Suitable for students in Grades 8-10.

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