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Algebra Difficulty 1.9 Junior Find the answer

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

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)(2,7) and (a,3a)(a, 3a) is 2, then 3a7a2=2\frac{3a-7}{a-2}=2. From this, 3a7=2(a2)3a-7=2(a-2) and so 3a7=2a43a-7=2a-4 which gives a=3a=3.

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