Example 1 Easy
If f(x) = 2x + 5, what is f(4)?
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- 13
- 18
Show answer and explanation
Answer: 13
Substitute x = 4 into the function: f(4) = 2(4) + 5 = 8 + 5 = 13.
SAT Math skill page
SAT Linear Functions Practice
Master slope, intercepts, and function notation so linear relationships feel predictable on SAT Math.
10-16 min practice time 3 examples on page Heart of Algebra
What this tests
What to know for this SAT skill
- Evaluate linear functions from equations
- Find slope from an equation, table, or two points
- Interpret y-intercepts and rates of change
- Use function notation without confusing inputs and outputs
Practice examples
Try a few SAT-style questions
Example 2 Medium
What is the slope of the line with equation y = 3x - 2?
- -2
- 1
- 2
- 3
Show answer and explanation
Answer: 3
In slope-intercept form y = mx + b, the coefficient of x is the slope. Here, m = 3.
Example 3 Hard
A line passes through (2, 5) and (6, 17). If the same line contains the point (10, y), what is y?
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- 29
- 32
Show answer and explanation
Answer: 29
The slope is (17 - 5) / (6 - 2) = 12 / 4 = 3. From x = 6 to x = 10, x increases by 4, so y increases by 12. Therefore y = 17 + 12 = 29.
Avoid these traps
Common mistakes on this skill
Mixing up slope and intercept
In y = mx + b, m is the rate of change and b is the starting value when x = 0.
Treating f(4) as multiplication
Function notation f(4) means the output when the input is 4, not f times 4.
Reading graph units too quickly
Check the scale on both axes before calculating slope from a graph.
Study plan
How to practice this skill in Dolphin
- Practice identifying slope and intercept from y = mx + b.
- Move between equations, tables, and points for the same line.
- Translate rates and starting values from word problems into linear equations.
- Review missed questions by naming which representation caused the mistake.
Related practice
Build the surrounding skills
FAQ
Questions about SAT Linear Functions Practice
What is the most important linear function idea for SAT Math?
Slope is the core idea. It represents rate of change and appears in equations, graphs, tables, and word problems.
Are linear functions different from linear equations?
They overlap. Linear functions emphasize inputs and outputs, while linear equations often focus on solving for an unknown.
How should I practice linear functions?
Practice switching formats: equation to graph, table to slope, and word problem to function rule.