SAT Math skill page

SAT Linear Functions Practice

Master slope, intercepts, and function notation so linear relationships feel predictable on SAT Math.

Practice linear functions in Dolphin Practice questions

10-16 min practice time3 questions on pageHeart of Algebra

Practice time10-16 min

Question bank3 questions

Best forHeart 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

Dolphin question bank

Practice your skill

Question 1 of 3Easy

Which table gives three values of x and their corresponding values of y for the given equation y = 70x + 8?

$x 024 y 8148288$
$x 024 y 87886$
$x 024 y 70140280$
$x 024 y 8132272$

Show answer and solution

Correct answerA. $x 024 y 8148288$

Solution walkthrough

Each of the given choices gives three values of $x$ : 0, 2, and 4. Substituting 0 for $x$ in the given equation yields $y = 70 (0) + 8$ , or $y = 8$ .
Therefore, when $x = 0$ , the corresponding value of $y$ for the given equation is 8. Substituting 2 for $x$ in the given equation yields $y = 70 (2) + 8$ , or $y = 148$ .
Therefore, when $x = 2$ , the corresponding value of $y$ for the given equation is 148. Substituting 4 for $x$ in the given equation yields $y = 70 (4) + 8$ , or $y = 288$ .
Therefore, when $x = 4$ , the corresponding value of $y$ for the given equation is 288.

Question 2 of 3Medium

According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of the bee, in grams. According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of 0.5 grams?

Show answer and solution

Correct answerD. 2.6

Solution walkthrough

The correct answer is 2.6. According to the model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to 4 times the body weight, in grams, of the bee.
Let $x$ represent the body weight, in grams, of a worker bumblebee and let $y$ represent the head width, in millimeters. Translating the verbal description of the model into an equation yields $y = 0.6 + 4 x$ .
Substituting 0.5 grams for $x$ in this equation yields $y = 0.6 + 4 (0.5)$ , or $y = 2.6$ . Therefore, a worker bumblebee with a body weight of 0.5 grams has an estimated head width of 2.6 millimeters.
Note that 2.6 and 13/5 are examples of ways to enter a correct answer.

Question 3 of 3Hard

According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the United States from September 1, 2014, to December 1, 2014, is modeled by the function F defined below, where F(x) is the average price per gallon x months after September 1. F(x) = 2.74 - 0.19(x - 3) The constant 2.74 in this function estimates which of the following?

The average monthly decrease in the price per gallon
The difference in the average price per gallon from September 1, 2014, to December 1, 2014
The average price per gallon on September 1, 2014
The average price per gallon on December 1, 2014

Show answer and solution

Correct answerD. The average price per gallon on December 1, 2014

Solution walkthrough

Since 2.74 is a constant term, it represents an actual price of gas rather than a measure of change in gas price.
To determine what gas price it represents, find $x$ such that $F (x) = 2.74$ , or $2.74 = 2.74 - 0.19 (x - 3)$ .
Subtracting 2.74 from both sides gives $0 = - 0.19 (x - 3)$ .
Dividing both sides by $- 0.19$ results in $0 = x - 3$ , or $x = 3$ .
Therefore, the average price of gas is $2.74$ per gallon 3 months after September 1, 2014, which is December 1, 2014.

Why the other choices miss

Choice A is incorrect. Since 2.74 is a constant, not a multiple of

x

, it cannot represent a rate of change in price. Choice B is incorrect. The difference in the average price from September 1, 2014, to December 1, 2014, is

F (3) - F (0) = 2.74 - 0.19 (3 - 3) - (2.74 - 0.19 (0 - 3)) = 2.74 - (2.74 + 0.57) = - 0.57

, which is not 2.74. Choice C is incorrect. The average price per gallon on September 1, 2014, is

F (0) = 2.74 - 0.19 (0 - 3) = 2.74 + 0.57 = 3.31

, which is not 2.74.

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.

Practice linear functions in Dolphin

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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.