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What are the x-intercept and y-intercept of the line 4x - 3y = 12?
Ax-intercept (-3, 0) and y-intercept (0, 4)
Bx-intercept (0, 3) and y-intercept (-4, 0)
Cx-intercept (3, 0) and y-intercept (0, -4)
Dx-intercept (4, 0) and y-intercept (0, -3)
Answer & Solution
Correct answer: C. x-intercept (3, 0) and y-intercept (0, -4)
1. To find the x-intercept, let y = 0: 4x - 3(0) = 12, so 4x = 12 and x = 3, giving the point (3, 0).
2. To find the y-intercept, let x = 0: 4(0) - 3y = 12, so -3y = 12 and y = -4, giving the point (0, -4).
3. The intercepts are the points (3, 0) and (0, -4).
4. Reversing which coordinate is zero, as in (0, 3) and (-4, 0), would place both intercepts on the wrong axis.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 4 "Graphs", section 4.3 Graph with Intercepts_
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