Question
3. \( -3 x+2 y=12 \) \( x \)-intercept: \( y \)-intercept:
Ask by Hamilton Olson. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The x-intercept is (-4, 0) and the y-intercept is (0, 6).
Solution
To find the intercepts of the line given by the equation -3x + 2y = 12, follow these steps:
1. x-intercept: Set y = 0 and solve for x.
-3x + 2(0) = 12
-3x = 12
x = -4
Thus, the x-intercept is (-4, 0).
2. y-intercept: Set x = 0 and solve for y.
-3(0) + 2y = 12
2y = 12
y = 6
Thus, the y-intercept is (0, 6).
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Simplify this solution Extra Insights
To find the \( x \)-intercept, set \( y = 0 \) in the equation \( -3x + 2y = 12 \). This gives you \( -3x = 12 \) or \( x = -4 \). So, the \( x \)-intercept is at \( (-4, 0) \). For the \( y \)-intercept, set \( x = 0 \) in the same equation, yielding \( 2y = 12 \) or \( y = 6 \). Therefore, the \( y \)-intercept is at \( (0, 6) \).
