To find the x- and y-intercepts of the line given by the equation \(2x + 3y = -18\), we can follow these steps:
1. Finding the x-intercept:
The x-intercept occurs when \(y = 0\). So we substitute \(y = 0\) into the equation:
\[ 2x + 3(0) = -18 \]
This simplifies to:
\[ 2x = -18 \]
Dividing both sides by 2:
\[ x = -9 \]
So the x-intercept is \((-9, 0)\).
2. Finding the y-intercept:
The y-intercept occurs when \(x = 0\). So we substitute \(x = 0\) into the equation:
\[ 2(0) + 3y = -18 \]
This simplifies to:
\[ 3y = -18 \]
Dividing both sides by 3:
\[ y = -6 \]
So the y-intercept is \((0, -6)\).
Conclusion
The x-intercept is \(-9\) and the y-intercept is \(-6\).
Thus, the correct option is:
x-intercept is -9; y-intercept is -6.