CEMC Cayley

Algebra Difficulty 1.9 Junior Find the answer

If the line that passes through the points $(2,7)$ and $(a, 3a)$ has a slope of 2, what is the value of $a$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the slope of the line through points $(2,7)$ and $(a, 3a)$ is 2, then $\frac{3a-7}{a-2}=2$ . From this, $3a-7=2(a-2)$ and so $3a-7=2a-4$ which gives $a=3$ .

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