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Digital SAT Math Practice Questions – Medium : Linear functions

SAT MAth Practice questions – all topics

  • Algebra Weightage: 35%  Questions: 13-15
    • Linear equations in one variable
    • Linear equations in two variables
    • Linear functions
    • Systems of two linear equations in two variables
    • Linear inequalities in one or two variables

SAT MAth and English  – full syllabus practice tests

Question Medium

Some values of the linear function \( f \) are shown in the table below:

\( x \)\( f(x) \)
0-2
24
616

What is the value of \( f(3) \)?

A) 6

B) 7

C) 8

D) 9

▶️ Answer/Explanation
Solution

Ans: B

Slope: \( \frac{4 – (-2)}{2 – 0} = 3 \)

From \( f(2) = 4 \), \( f(3) = 4 + 3 = 7 \)

Question Medium

The graph above shows the distance traveled \( d \), in feet, by a product on a conveyor belt \( m \) minutes after the product is placed on the belt. Which of the following equations correctly relates \( d \) and \( m \)?

Graph of Distance vs Time on Conveyor Belt

A) \( d = 2m \)

B) \( d = \frac{1}{2}m \)

C) \( d = m + 2 \)

D) \( d = 2m + 2 \)

▶️ Answer/Explanation
Solution

Ans: A

Line passes through origin, so \( d = km \)

Using point \( (2, 4) \): \( 4 = k \cdot 2 \), \( k = 2 \)

Equation: \( d = 2m \)

Question Medium

The graph of the function \( f \), where \( y = f(x) \), gives the total cost \( y \), in dollars, for a certain video game system and \( x \) games. What is the best interpretation of the slope of the graph in this context?

Graph of Total Cost vs Number of Games

A) Each game costs $25

B) The video game system costs $100

C) The video game system costs $25

D) Each game costs $100

▶️ Answer/Explanation
Solution

Ans: A

Slope = change in cost per game: \( \frac{125 – 100}{1 – 0} = 25 \)

Each game costs $25

Question Medium

Some values of \(\mathrm{x}\) and the corresponding values of \(f(x)\) are given in the table shown.

\(x\)\(f(x)\)
21
51.5
82
112.5

If there is a linear relationship between \(\mathrm{x}\) and \(f(\mathrm{x})\), which of the following equations gives this relationship?

A) \(f(x)=\frac{1}{2} x+\frac{1}{2}\)

B) \(f(x)=\frac{1}{2} x-\frac{1}{2}\)

C) \(f(x)=\frac{1}{6} x+\frac{5}{6}\)

D) \(f(x)=\frac{1}{6} x+\frac{2}{3}\)

▶️ Answer/Explanation
Solution

Answer: D

Use point-slope form: \( f(x) – f(x_1) = m(x – x_1) \)

Choose point \((2, 1)\)

Calculate slope \( m \) using \((5, 1.5)\):

\( m = \frac{1.5 – 1}{5 – 2} = \frac{0.5}{3} = \frac{1}{6} \)

Substitute \( m = \frac{1}{6} \) and \((2, 1)\):

\( f(x) – 1 = \frac{1}{6}(x – 2) \)

\( f(x) – 1 = \frac{1}{6}x – \frac{1}{3} \)

\( f(x) = \frac{1}{6}x – \frac{1}{3} + 1 \)

\( f(x) = \frac{1}{6}x + \frac{2}{3} \)

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