8
algebra

A line has a slope of 23-\frac{2}{3} and passes through the origin. What is its equation?

A

y=23xy = -\frac{2}{3}x

B

y=23x+1y = -\frac{2}{3}x + 1

C

y=23xy = \frac{2}{3}x

D

y=x23y = x - \frac{2}{3}

Correct Answer: A

Choice A is the correct answer. The origin is (0,0)(0, 0).

  1. Intercept: Passing through the origin means the y-intercept b=0b = 0.
  2. Slope: m=23m = -\frac{2}{3}.
  3. Equation: y=23x+0y = -\frac{2}{3}x + 0, or y=23xy = -\frac{2}{3}x.

💡 Strategic Tip: Direct variation equations (y=kxy=kx) always pass through the origin.

Choice B is incorrect because it has a y-intercept of 1. Choice C is incorrect because it has the wrong slope sign. Choice D is incorrect because it puts the slope in the intercept position.