8
algebra

Write the equation of the line passing through (4,0)(4, 0) and (0,3)(0, 3).

A

y=−34x+3y = -\frac{3}{4}x + 3

B

y=34x+3y = \frac{3}{4}x + 3

C

y=−43x+3y = -\frac{4}{3}x + 3

D

y=−34x+4y = -\frac{3}{4}x + 4

Correct Answer: A

Choice A is the correct answer. Use intercepts.

  1. Y-intercept: (0,3)→b=3(0, 3) \rightarrow b = 3.
  2. Slope: 3−00−4=3−4=−34\frac{3 - 0}{0 - 4} = \frac{3}{-4} = -\frac{3}{4}.
  3. Equation: y=−34x+3y = -\frac{3}{4}x + 3.

💡 Strategic Tip: Intercept form is x/a+y/b=1x/a + y/b = 1. Here x/4+y/3=1→3x+4y=12→y=−3/4x+3x/4 + y/3 = 1 \rightarrow 3x + 4y = 12 \rightarrow y = -3/4x + 3.

Choice B is incorrect because slope sign error. Choice C is incorrect because rise/run flip. Choice D is incorrect because intercept error.

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