Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.
Find an exact intersection by solving f(x) = g(x)
Problem
Find the exact intersection of \(y~=~2x~+~1\) and \(y~=~-x~+~7\).
Big Picture
What this problem is really about
At an intersection, the two rules produce the same output from the same input. We’ll set their output expressions equal and solve that equation for the shared input, then substitute it into either rule to recover the shared output. Checking the point in both original rules confirms the crossing, and writing both coordinates avoids stopping with only half of the intersection.
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