Back to Explain intersection as solution — Problem 2 · 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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$Coordinate plane showing two curves intersecting at the point (3, 7). Dashed lines drop from the intersection to x = 3 on the x-axis and to y = 7 on the y-axis. The x-axis label shows 'solution = x = 3' and the y-axis label shows 'shared output = 7'.$

The graphs of $y = f(x)$ and $y = g(x)$ intersect at the point $(3, 7)$ .

What is the solution to the equation $f(x) = g(x)$ ?

$x = 3$

$x = 7$

$x = 3$ and $y = 7$

$(3, 7)$