Two lines y = 2x + 3 and y = -x + 9 intersect at which coordinates?

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Two lines y = 2x + 3 and y = -x + 9 intersect at which coordinates?

Explanation:
Intersections happen where two lines share a point, so the coordinates must make both line equations true at the same time. For these lines, y is given by 2x + 3 on the first and -x + 9 on the second. At the intersection these y-values are equal, so set 2x + 3 = -x + 9. Solve: 2x + 3 = -x + 9 → add x to both sides: 3x + 3 = 9 → subtract 3: 3x = 6 → x = 2. Now plug x = 2 into either equation to find y: y = 2(2) + 3 = 7, and the other equation gives y = -2 + 9 = 7, which matches. So the intersection is at (2, 7).

Intersections happen where two lines share a point, so the coordinates must make both line equations true at the same time. For these lines, y is given by 2x + 3 on the first and -x + 9 on the second. At the intersection these y-values are equal, so set 2x + 3 = -x + 9. Solve: 2x + 3 = -x + 9 → add x to both sides: 3x + 3 = 9 → subtract 3: 3x = 6 → x = 2. Now plug x = 2 into either equation to find y: y = 2(2) + 3 = 7, and the other equation gives y = -2 + 9 = 7, which matches. So the intersection is at (2, 7).

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