To find the x- and y-intercepts of the line given by the equation \(-3x + 9y = 18\), we can follow these steps:
1. Finding the x-intercept:
To find the x-intercept, set \(y = 0\) and solve for \(x\):
\[ -3x + 9(0) = 18 \]
This simplifies to:
\[ -3x = 18 \]
Dividing both sides by -3:
\[ x = -6 \]
So, the x-intercept is \((-6, 0)\).
2. Finding the y-intercept:
To find the y-intercept, set \(x = 0\) and solve for \(y\):
\[ -3(0) + 9y = 18 \]
This simplifies to:
\[ 9y = 18 \]
Dividing both sides by 9:
\[ y = 2 \]
So, the y-intercept is \((0, 2)\).
Summary:
- The x-intercept is \(-6\).
- The y-intercept is \(2\).
Therefore, the correct answer is: x-intercept is –6; y-intercept is 2.