SAT Linear equations in two variables Practice Question 19 (Hard)

Question bank / Linear equations in two variables

Math · AlgebraHard

In the $xy$ -plane, the graph of $5x + 3y = 45$ and the two coordinate axes form a triangle. What is the area of this triangle?

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Answer: 135/2

The $x$ -intercept is found by setting $y = 0$ : $x = 9$ . The $y$ -intercept is found by setting $x = 0$ : $y = 15$ . The triangle is a right triangle with legs 9 and 15, so its area is $\frac{1}{2}(9)(15) = 67.5$ .

Forgetting the $\frac{1}{2}$ in the triangle area formula gives 135.

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