1971 AHSME Problems/Problem 3

Problem 3

If the point $(x,-4)$ lies on the straight line joining the points $(0,8)$ and $(-4,0)$ in the $xy$ -plane, then $x$ is equal to

$\textbf{(A) }-2\qquad \textbf{(B) }2\qquad \textbf{(C) }-8\qquad \textbf{(D) }6\qquad \textbf{(E) }-6$

Solution

Since $(x,-4)$ is on the line $(0,8)$ and $(-4,0)$ , the slope between the latter two is the same as the slope between the former two, so $\frac{-4-8}{x-0}=\frac{8-0}{0-(-4)}$ . Solving for $x$ , we get $x=-6$ , so the answer is $\textbf{(E)}$ .

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1971 AHSME Problems/Problem 3

Problem 3

Solution