What you’ll learn
Interpret intersections as equation solutions.
Key idea
Equality of function outputs means equal vertical heights at the same horizontal input.
Intersection height is not the input solving output equality; both labels and common coordinate are needed.
Worked example
Enter the exact value or ordered values in the format requested below.
F and H are straight lines through their repeated marks, C shared. Read the numerical x solving F(x)=H(x), not the height. x horizontal, y vertical.
Marked coordinates: F=(-4, 10); F=(-3, 7); H=(-4, 4); H=(-3, 4); C=(-2, 4); H=(-1, 4); H=(0, 4); F=(-1, 1); F=(0, -2).
- F has equation y=-3x-2 and H has equation y=4. Their common point is (-2,4).
- Equal outputs require -3x-2=4; isolating x gives -2. The equation solution is its horizontal coordinate, not height 4.
Answer: -2
Quick Check
Relate the graph used in 'Interpret intersections as equation solutions' to an equation, table, transformation, or verbal description.
Connect the intersection of these full straight graphs to an equation and its numerical x solution. C shared, x horizontal, y vertical.
Marked coordinates: F=(0, 2); F=(1, -1); H=(0, -4); H=(1, -4); C=(2, -4); H=(3, -4); H=(4, -4); F=(3, -7); F=(4, -10).