Back to Explain intersection as solution — Problem 3 · Task Set 52

Exercises: Graph Intersections as Solutions

For graphical problems, identify the x-coordinate of each intersection as the solution. Always verify by substituting back into both sides of the original equation. Use graphing technology (Desmos or graphing calculator) where indicated.

Grade 9·18 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-d-11

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Recall / Warm-Up

A student graphs $y = 2x + 1$ and $y = 5$ on the same axes. The two graphs intersect at the point $(2, 5)$ .

What can the student conclude?

$x = 5$ satisfies $2x + 1 = 5$ .

$x = 2$ satisfies $2x + 1 = 5$ .

There is no solution because $2x + 1 \neq 5$ for any real $x$ .

$y = 5$ is the solution to $2x + 1 = 5$ .