The use of graphs and/or pictures as the main technique
for solving a math problem. When a problem is solved graphically,
it is common to use a graphing calculator.
Problem: Solve the system of equations graphically: y = x + 1 and y = -x + 5.
Step 1: Graph the first equation. It is a line with slope 1 and y-intercept 1.
y=x+1
Step 2: Graph the second equation on the same axes. It is a line with slope −1 and y-intercept 5.
y=−x+5
Step 3: Identify the point where the two lines cross. Reading from the graph, the lines intersect at the point (2, 3).
(2,3)
Answer: The solution is x = 2, y = 3, found by locating the intersection point on the graph.
Why It Matters
Graphic methods let you see the behavior of functions — where they increase, decrease, or intersect — in a way that pure algebra cannot. They are especially useful when an equation has no neat algebraic solution, such as finding where y=ex meets y=3x. Many standardized tests and real-world applications rely on graphical reasoning to estimate solutions quickly.
Common Mistakes
Mistake: Reading intersection points imprecisely and reporting approximate answers as exact.
Correction: Graphic methods often yield estimates. If the problem requires an exact answer, verify your graphical solution by substituting the values back into the original equations or use an analytic method to confirm.
Related Terms
Analytic Methods — Algebraic alternative to solving problems graphically
Mathwords