Linear functions and graphs — ACT practice questions

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Practice 40 Linear functions and graphs questions in the app

What this topic is

Slope and intercept carry the meaning in Linear functions and graphs.

A linear function changes by the same amount for each step in x, so it can be written as y = mx + b, where m is that fixed change and b is the starting value. In a word problem, the slope is a rate, such as dollars per month, and the intercept is the initial amount.

ACT Mathematics asks for an equation built from a table or pattern, an interpretation of the numbers in a model, or an average rate of change, which is the change in output divided by the change in input.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A small theater has 18 seats in row 1, 24 seats in row 2, 30 seats in row 3, and 36 seats in row 4. If the number of seats continues to increase by 6 per row, which of the following equations gives the number $S (r)$ of seats in row $r$ ?

S (r) = 6 r + 18

✗ Not this one

S (r) = 18 r + 6

✗ Not this one

S (r) = 18 r - 6

✗ Not this one

S (r) = 6 r + 12

✓ Correct

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Answer: D — $S (r) = 6 r + 12$

The increase of 6 seats per row gives a coefficient of 6. Since S(1) = 18, the constant must be 12, so S(r) = 6r + 12.

Question 2Easier

The number of loaves a bakery sells monthly is modeled by $L (m) = 210 + 39 m$ , where $m$ is the number of months after the first month. Which of the following statements correctly interprets the numbers in this model?

The bakery sells 210 loaves in the first month and then 39 more loaves each month.✓ CorrectThe bakery sells 39 loaves in the first month and then 210 more loaves each month.✗ Not this oneThe bakery sells 39 loaves in the first month and then 210 fewer loaves each month.✗ Not this oneThe bakery sells 210 loaves in the first month and then 39 fewer loaves each month.✗ Not this one

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Answer: A — The bakery sells 210 loaves in the first month and then 39 more loaves each month.

Because m = 0 represents the first month, 210 is the starting value. The coefficient 39 means monthly sales increase by 39 loaves per month.

Question 3Mid

For $f (x) = 2 x^{2} - 3 x + 1$ , what is the average rate of change of $f$ from $x = 1$ to $x = 4$ ?

3✗ Not this one5✗ Not this one7✓ Correct9✗ Not this one

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Answer: C — 7

The function values are $f (1) = 0$ and $f (4) = 21$ . The average rate of change is $\frac{21 - 0}{4 - 1} = 7$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 40 Linear functions and graphs questions in the app

Linear functions and graphs — ACT practice questions

What this topic is

Sample questions

More ACT topics

Mathematics