AnswersAISD Algebraic Reasoning A Credit Recovery 2026-2027Modeling Functions Using Finite Differences

Writing Linear Equations Answers

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The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.What is the cost of a pizza with 5 toppings? Round to the nearest penny.

A
$19.00
B
$22.75
C
$43.75
D
$70.00
2
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The slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?

A
y – 13 = 5(x – 2)
B
y + 13 = 5(x + 2)
C
y – 2 = 5(x – 13)
D
y + 2 = 5(x + 13)
3

Tim explained a function in words and Paul wrote an equation.TimThe amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. Pauly−1,400=56(x+26)Whose function has the smaller y-intercept?

A
Tim’s with a y-intercept of $2,700
B
Paul’s with a y-intercept of $2,856
C
Paul’s with a y-intercept of $2,800
D
Tim’s with a y-intercept of $2,780
4

The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?

A
c(x) = 3x + 3
B
c(x) = 6x + 3
C
c(x) = 7x + 3
D
c(x) = 8x + 3
5

The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?

A
y = 12x + 8
B
y = 12x − 8
C
y = 14x + 8
D
y = 14x − 8
6

Line CD passes through points C(1, 3) and D(4, –3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

A
–5
B
–2
C
1
D
5
7

Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?

A
y = 2x – 2
B
y = 2x + 2
C
y = x + 2
D
y = x – 2
8

The table represents a linear equation.

Question illustration
A
y – 8 = –0.15(x – 10)
B
y + 8 = –0.15(x – 10)
C
y – 8 = –0.2(x + 10)
D
y + 8 = –0.2(x – 10)
9

The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –x + 6. What is the point-slope form of the equation for this line?

Question illustration
A
y – 3 = –(x + 8)
Option A
B
y + 3 = –(x – 8)
Option B
C
y + 8 = –(x – 3)
Option C
D
y – 8 = –(x + 3)
Option D
10

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable.Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes?

A
k – 2 = (t – 18)
Option A
B
k – 18 = (t – 2)
Option B
C
k – 2 = 9(t – 18)
D
k – 18 = 9(t – 2)

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