Question

Which equation represents the line that passes through points (0, 6) and (2, 0)? A.)y = negative one-third x + 2 B.)y = negative one-third x + 6 c.)y = negative 3 x + 2 D.)y = negative 3 x + 6 pls help quickly

Answer 1

Find the slope of the line through (x1,y1) = (0,6) and (x2,y2) = (2,0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(2 - 0)

m = -6/2

m = -3

The slope is -3

Since we're given the point (0,6) to be on the line, we know the y intercept is b = 6.

Plug m = -3 and b = 6 into y = mx+b to get y = -3x+6

Answer: Choice D)  y = -3x+6

Answer 2

$(A)\;\; y = \frac{-x}{3} + 2\\(B)\;\; y = \frac{-x}{3} + 6\\(C)\;\; y = -3x + 2\\(D) \;\; y = -3x + 6$

The correct option is D.

What is the equation of a straight line passing through two points?

The equation of a straight line passing through points (x₁, y₁), (x₂, y₂) is

$\frac{y-y_1}{x-x_1} = \frac{y_2 - y_1}{x_2 - x_1}.$

Given

Two points: A₁(0,6), A₂(2,0)

Find the equation of the straight line

Using the above formula, the equation of the straight line passing through points (0,6), (2,0) is

$\frac{y-6}{x-0} = \frac{0-6}{2-0}\\ \\\Rightarrow\;\; \frac{y-6}{x} = -3\\ \\\Rightarrow\;\; y = -3x + 6.$

The option which matches this equation is D.

Equation D represents the straight line passing through the points (0,6), (2,0).

Learn more about the equations of straight lines here

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