SAT Linear equations in two variables Practice Question 14 (Medium)

Question bank / Linear equations in two variables

Math · AlgebraMedium

A line in the $xy$ -plane has a slope of $\frac{3}{2}$ and passes through the point $(4, 1)$ . If the point $(10, k)$ also lies on the line, what is the value of $k$ ?

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Answer: 10

Moving from $x = 4$ to $x = 10$ is a change of 6. With slope $\frac{3}{2}$ , $y$ changes by $\frac{3}{2}(6) = 9$ . So $k = 1 + 9 = 10$ .

Multiplying 6 by $\frac{2}{3}$ instead of $\frac{3}{2}$ gives $k = 5$ .

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