Mississippi Math A-REI.11

MathGrades 9–12Seeing Structure in Expressions

The Standard

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential functions. *

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Represent and Solve Equations and Inequalities Graphically

Teacher's field guide

What This Standard Means

What Students Need to Do: Students graph two functions and find the x-values where the graphs meet. They use a graph or table to estimate solutions when the x-values are not whole numbers.
What Mastery Looks Like: A student can explain that, at an intersection, both functions give the same y-value for one x-value. They can find every intersection and report its x-value, including an estimate when needed.
Common Misconceptions: Students may report the y-value at an intersection instead of the x-value. They may stop after finding one intersection or assume an estimate from a graph is exact.
How to Assess It: Have students graph y = x² and y = x + 1 on a calculator. Ask for both intersection x-values to the nearest tenth and one sentence explaining why they solve the equation.

Lesson moves

Ways to Teach It

Have students plot y = x² and y = x + 2 on separate transparencies, then overlay them and read both intersection x-values.
Ask: At x = 2, both 2^x and x + 2 equal 4. Why is 2 a solution, but 4 is not?
Give pairs a table for y = |x − 1| and y = 2 at integer x from −2 to 4; race to find matching outputs.
Plot two phone plans, $20 plus $5 per GB and $35 plus $2 per GB, and mark the data use where costs match.

Free download