Interpreting Graphs on the SAT
Read the Story, Not Just the Picture
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Interpreting Graphs
Graph interpretation questions are about reading a story from a picture. The SAT often asks for the rate of change, the intercept, or the meaning of a point on the graph.
This lesson shows how to identify what each axis represents, how to compute or read slope, and how to translate a coordinate into a sentence that matches the real world context.
A Simple Definition Unlocks Interpreting Graphs
Start by reading the axes, units, and labels. Those details tell you what each coordinate represents. A point like $(3, 12)$ might mean $3$ months and $12$ dollars, or $3$ hours and $12$ miles, depending on the prompt.
The slope tells you the rate of change. The intercept tells you the starting value when the input is $0$. If the graph is a curve, interpret average rate over an interval instead of assuming a constant slope.
Work Through Interpreting Graphs Step by Step
What is the slope of the line through $(0, 2)$ and $(5, 12)$?
Use two points to interpret a rate of change, then describe what that rate means in context.
Use points $(0, 2)$ and $(5, 12)$
Compute the rate so you can interpret the slope.
Simplify the expression to make the next step clear.
Use Desmos to Check Interpreting Graphs
What is the slope of the line through $(0, 2)$ and $(5, 12)$?
Desmos can display the slope between two points if you define them and use the slope formula. This is helpful when the graph has messy coordinates.
m = (y2 - y1) / (x2 - x1)
Algebra is faster for simple points. Desmos is helpful for verifying or reading exact values from a complex graph.
Desmos is faster when you need to recreate a graph from an equation. Algebra is faster when the graph is already provided and you just need to read it.
Expert move: Graph the key functions together and use intercepts or a table to compare how values change; Desmos makes the shape (linear vs exponential, shifts, stretches) obvious.
Reminder: Desmos confirms the picture, but you still have to interpret axes, units, and context.
- Desmos features used: point evaluation, slope calculation.
- Common mistake: reading $x$ and $y$ values from the wrong tick marks.
Practice Interpreting Graphs with SAT-Style Questions
Interpret the graph and its key features.
A line passes through and . What is the slope?
What does the point mean on a graph of vs. ?
If a line has intercept , what point lies on the line?
A graph shows a line with slope . What does that mean?
Key Takeaways to Remember for Interpreting Graphs
- Intercepts show starting values and where graphs cross axes.
- Slopes tell you the rate of change.
- Desmos can confirm slopes and points quickly.
About the Instructor
