Question

4.
Find the x- and y-intercept of the line.

2x + 3y = –18



x-intercept is –6; y-intercept is –9.


x-intercept is 18; y-intercept is 18.


x-intercept is –9; y-intercept is –6.


x-intercept is 2; y-intercept is 3.

Answer 1

To find the x- and y-intercepts of the line represented by the equation \(2x + 3y = -18\), we can follow these steps:

1. **Finding the x-intercept**: This occurs where \(y = 0\).
\[
2x + 3(0) = -18 \\
2x = -18 \\
x = -9
\]

Thus, the x-intercept is \((-9, 0)\).

2. **Finding the y-intercept**: This occurs where \(x = 0\).
\[
2(0) + 3y = -18 \\
3y = -18 \\
y = -6
\]

Thus, the y-intercept is \((0, -6)\).

Now we can summarize the results:
- The x-intercept is \(-9\).
- The y-intercept is \(-6\).

Therefore, the correct answer is:
**x-intercept is –9; y-intercept is –6.**