5. which situation represents a linear relationship?
a. the value of a car decreasing faster each year
b. a straight - line graph with constant change
c. a curved graph showing growth
d. a table with inconsistent differences

6. which relation is not a function?
a. {(1,2), (2,3), (3,4)}
b. {(2,5), (2,7), (4,9)}
c. {(0,1), (1,1), (2,1)}
d. {(5,3), (6,4), (7,5)}

7. a concert hall can seat 4,000 people. tickets cost $25.
what is the domain of the function?
a. 0 ≤ p ≤ 100,000
b. 0 ≤ p ≤ 4,000, where p is an integer
c. 0 ≤ p ≤ 100,000
d. all real numbers

8. a graph shows distance remaining to school over time.
what does the slope represent?
a. total distance
b. speed toward school
c. starting distance
d. time traveled

9. maya charges $1.75 per bracelet. a graph shows jordan charges $2.25 per bracelet.
which statement is correct?
a. maya charges $0.50 more
b. jordan charges $0.50 more
c. maya charges $0.25 more
d. jordan charges $0.25 more

10. a landscaper charges $65 plus $30 per hour.
which equation models the cost c for h hours?
a. c = 30h + 65
b. c = 65h + 30
c. c = 65 - 30h
d. 30h - c = - 65

Question

5. which situation represents a linear relationship?
a. the value of a car decreasing faster each year
b. a straight - line graph with constant change
c. a curved graph showing growth
d. a table with inconsistent differences

6. which relation is not a function?
a. {(1,2), (2,3), (3,4)}
b. {(2,5), (2,7), (4,9)}
c. {(0,1), (1,1), (2,1)}
d. {(5,3), (6,4), (7,5)}

7. a concert hall can seat 4,000 people. tickets cost $25.
what is the domain of the function?
a. 0 ≤ p ≤ 100,000
b. 0 ≤ p ≤ 4,000, where p is an integer
c. 0 ≤ p ≤ 100,000
d. all real numbers

8. a graph shows distance remaining to school over time.
what does the slope represent?
a. total distance
b. speed toward school
c. starting distance
d. time traveled

9. maya charges $1.75 per bracelet. a graph shows jordan charges $2.25 per bracelet.
which statement is correct?
a. maya charges $0.50 more
b. jordan charges $0.50 more
c. maya charges $0.25 more
d. jordan charges $0.25 more

10. a landscaper charges $65 plus $30 per hour.
which equation models the cost c for h hours?
a. c = 30h + 65
b. c = 65h + 30
c. c = 65 - 30h
d. 30h - c = - 65

Accepted Answer

### Question 5
# Brief Explanations:
A linear relationship has a constant rate of change. A straight - line graph with constant change (slope) represents a linear relationship. Option A has a non - constant rate (decreasing faster each year), Option C is a curved graph (non - linear), and Option D has inconsistent differences (non - linear).
# Answer: B. A straight - line graph with constant change

### Question 6
# Brief Explanations:
A function is a relation where each input (x - value) has exactly one output (y - value). In option B, the input $x = 2$ has two outputs ($y=5$ and $y = 7$), so it is not a function. In options A, C, and D, each $x$ - value has only one $y$ - value.
# Answer: B. $\{(2,5),(2,7),(4,9)\}$

### Question 7
# Brief Explanations:
The domain of the function represents the number of people ($p$) that can attend the concert. The concert hall can seat at most 4000 people, and the number of people must be a non - negative integer (you can't have a fraction of a person). So $0\leq p\leq4000$, where $p$ is an integer. Option A and C have an upper limit of 100000 which is incorrect, and Option D (all real numbers) is wrong as the number of people must be a non - negative integer within the seating capacity.
# Answer: B. $0\leq p\leq4000$, where $p$ is an integer

### Question 8
# Brief Explanations:
The graph shows distance remaining to school over time. The slope of a distance - time graph is $\frac{\text{change in distance}}{\text{change in time}}$. Since it's distance remaining, a negative slope (as time increases, distance remaining decreases) would have a magnitude equal to the speed toward school. Total distance is the y - intercept (starting distance), and time traveled is the x - value.
# Answer: B. Speed toward school

### Question 9
# Brief Explanations:
To find the difference in charges, we subtract Maya's charge from Jordan's charge: $2.25−1.75 = 0.50$. So Jordan charges $\$0.50$ more than Maya.
# Answer: B. Jordan charges $\$0.50$ more

### Question 10
# Brief Explanations:
The landscaper charges a fixed fee of $\$65$ plus $\$30$ per hour. If $h$ is the number of hours, the cost $C$ is given by the equation $C=30h + 65$. We can also rewrite option D: $30h - C=- 65$ is equivalent to $C = 30h+65$ (by adding $C$ and 65 to both sides). Wait, let's check again. The correct model is $C=30h + 65$ (Option A) and also $30h - C=-65$ (Option D) is equivalent. Wait, no, let's re - evaluate. The fixed cost is 65, and the variable cost is $30h$ (30 dollars per hour). So $C=30h + 65$ can be rewritten as $30h - C=-65$ (subtract $C$ and 65 from both sides). But let's check the options. Option A: $C = 30h+65$ is correct. Option D: $30h - C=-65$ is also correct? Wait, no, maybe I made a mistake. Wait, the problem says "Which equation models the cost $C$ for $h$ hours?". The cost is fixed cost plus variable cost. Fixed cost is 65, variable cost is $30h$, so $C = 30h+65$ (Option A) and rearranging $30h - C=-65$ (Option D) is also correct? Wait, no, let's check the options again. Option A: $C = 30h + 65$ is the standard form. Option D: $30h - C=-65$ is the same as $C=30h + 65$ (add $C$ and 65 to both sides). But maybe the question considers Option A as the more direct model. Wait, let's check the arithmetic. If $h = 1$, cost should be $30(1)+65=95$. For Option A: $C = 30(1)+65 = 95$, correct. For Option D: $30(1)-C=-65\Rightarrow30 - C=-65\Rightarrow C=30 + 65=95$, also correct. But maybe the intended answer is A. Wait, let's check the options again. The problem says "Which equation models the cost $C$ for $h$ hours?". The fixed cost is 65, and the cost per hour is 30, so $C=30h + 65$ (Option A) and $30h - C=-65$ (Option D) are equivalent. But maybe in the context of the question, Option A is the more straightforward answer.
# Answer: A. $C = 30h+65$ and D. $30h - C=-65$ (but if we consider the standard form, A is more direct. However, mathematically both A and D are correct. But let's check the original options again. The question is likely expecting A as the answer as it is the slope - intercept form of the linear equation where 65 is the y - intercept (fixed cost) and 30 is the slope (cost per hour)).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 5

Answer:

Question 6