Bunuel wrote:

A line segment containing the point (0,0) and (12,8) will also contain the point

(A) (2,3)

(B) (2,4)

(C) (3,2)

(D) (3,4)

(E) (4,2)

Given that one point is (0,0): If a line runs though the origin, its x- and y-intercepts = 0, and vice versa.

In slope-intercept form, the line's equation is

y = mx + b

in which m = slope and "+ b" is not written because

b = y-intercept = 0

Use the two points to find slope, \(\frac{rise}{run}\)

\(\frac{(y_1 - y_2)}{(x_1 -

x_2)}=\frac{(8-0)}{(12-0)}=\frac{8}{12}=\frac{2}{3}\) = slope

Line's equation is

\(y=\frac{2}{3}x\)That's straightforward. The y-coordinate must be 2/3 of the x-coordinate.

That is (3,2) Answer C

*Or, rewrite equation of line:

\(y=\frac{2}{3}x\)

\(3y=2x\)

\(3y - 2x = 0\)

Plug x and y from each answer into the equation. The pair that = 0 is the answer.
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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"