Title: Fourth Partial exam
Course: 2025 Probabilidad y Estadística

Q: The slope of the line y = [Image] is [Image].
- True
- False
A: False

Q: The y-intercept of the line y = -1 - 9x is (0, - 9).
- True
- False
A: False

Q: A water tank is being drained at the rate of 17 gal/min. The tank started with 17750 gallons of water. Which of the following linear functions model the number of gallons of water in the tank at any time t.

​
- ​g​ = 17 + 17750​​t (Incorrect)
- g = - 17t (Incorrect)
- ​g​ = 17 - 17750t (Incorrect)
- ​g​ = 17750 - 17t (Correct)
- ​g​ = 17750 + 17​t (Incorrect)
A: ​g​ = 17750 - 17t

Q: A beanstalk grows at a constant rate. The beanstalk's height (inches) as a function of time (days) is modeled by ​h​ = 6 + 0.75​t​. What is the beanstalk's initial height?

​
- 6.75 inches (Incorrect)
- 6 inches (Correct)
- 0.75 inches (Incorrect)
- 0 inches (Incorrect)
- Not enough information (Incorrect)
A: 6 inches

Q: A beanstalk grows at a constant rate. The beanstalk's height (inches) as a function of time (days) is modeled by ​h​  = 4 + 1.15t. Which of the following graphs illustrate the function h?

​
- [Image] (Correct)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- None of these options (Incorrect)
A: [Image]

Q: Determine the correct equation for the line whose graph is sketched below.

​

[Image]

​
- y = -4x - 32 (Incorrect)
- y = 4x - 32 (Incorrect)
- [Image] (Incorrect)
- y = 4x - 32 (Incorrect)
- y = -4x + 32 (Correct)
A: y = -4x + 32

Q: Determine the correct equation for the line passing through the point (-5, -14) with a slope of 3.

​
- y = -3x - 1 (Incorrect)
- y = -3x + 1 (Incorrect)
- y = 3x+ 1 (Correct)
- y = 3x ​- 1 (Incorrect)
- [Image] (Incorrect)
A: y = 3x+ 1

Q: Determine the correct equation for the line passing through the point (3, 16) and the point (17, 3).

​
- 14y + 13x - 263 = 0 (Correct)
- 14y - 13x - 263 = 0 (Incorrect)
- 14y + 13x + 263 = 0 (Incorrect)
- 14y - 13x + 263 = 0 (Incorrect)
- none of these (Incorrect)
A: 14y + 13x - 263 = 0

Q: Determine the correct equation for the line with a slope of 6 and a y-intercept of -4.

​
- [Image] (Incorrect)
- y = -6x + 4 (Incorrect)
- [Image] (Incorrect)
- y = 6x - 4 (Correct)
- y = 6x + 4 (Incorrect)
A: y = 6x - 4

Q: Determine the correct equation for the line with an x-intercept of -2 and a y-intercept of 8.

​
- y = -4x + 8 (Incorrect)
- y = 4x - 8 (Incorrect)
- y = 4x + 8 (Correct)
- [Image] (Incorrect)
- [Image] (Incorrect)
A: y = 4x + 8

Q: Determine the correct equation for the line passing through the point (4, -4) and parallel to the line

x + 2y = 10.

​
- [Image] (Correct)
- y = 2x - 2 (Incorrect)
- [Image] (Correct)
- [Image] (Incorrect)
- y = 2x + 2 (Incorrect)
A: [Image] / [Image]

Q: Find an equation for the line that passes through the point (6, 3) and is perpendicular to the line x - 3y + 26 = 0.

​
- [Image] (Incorrect)
- y = 3x + 18 (Incorrect)
- y = 21 - 3x (Correct)
- y = x + 6 (Incorrect)
- [Image] (Incorrect)
A: y = 21 - 3x

Q: Determine the correct equation for the line passing through the point (2, 3) which is parallel to the line passing through both of the points (6, 7) and (-2, 71).

​
- y = -8x - 19 (Incorrect)
- [Image] (Incorrect)
- [Image] (Incorrect)
- y = -8x + 19 (Correct)
- [Image] (Incorrect)
A: y = -8x + 19

Q: Find the slope and the y-intercept of the line [Image] and draw its graph.

​
- m = 1, y-intercept = 12 [Image] (Incorrect)
- m = -1, y-intercept = 0 [Image] ​ (Incorrect)
- [Image] [Image] ​ (Incorrect)
- [Image] [Image] ​ (Incorrect)
- [Image] [Image] ​ (Correct)
A: [Image] [Image] ​

Q: The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the equation:

​

[Image]

​

Find the Celsius temperature corresponding to F = 95º.

​
- C = 34º (Incorrect)
- C = 35º (Correct)
- C = 37º (Incorrect)
- C = 33º (Incorrect)
- C = 36º (Incorrect)
A: C = 35º

Q: At the surface of the ocean, the water pressure is the same as the air pressure above the water, 4.48 lb/in.^2 Below the surface, the water pressure increases by 21 lb/in.^2 for every 10 feet of descent.

​

Determine the correct equation for the relationship between pressure (P) and depth (d) below the ocean surface where pressure is in lb/in.^2 and depth is in feet.

​
- P = 0.448d + 21 (Correct)
- P = 0.348d - 21 (Incorrect)
- P = 0.348d + 21 (Incorrect)
- P = -0.448d - 21 (Incorrect)
- P = -0.448d + 21 (Incorrect)
A: P = 0.448d + 21

Q: Determine the correct equation for the line passing through the point (1, 8) with a slope of 5.

​
- y = -3x ​- 5 (Incorrect)
- y = 5x + 3 (Correct)
- [Image] (Incorrect)
- y = 3x + 5 (Incorrect)
- y = -5x + 3 (Incorrect)
A: y = 5x + 3

Q: Determine the correct equation for the line whose graph is sketched below.

​

[Image]

​
- y = -6x + 36 (Incorrect)
- y = 6x - 36 (Correct)
- y = 6x + 36 (Incorrect)
- ​ [Image] (Incorrect)
- y = -6x - 36 (Incorrect)
A: y = 6x - 36

Q: Find the slope and y-intercept for the line x + y = 6 and draw its graph.

​
- m = -2, y = 0 [Image] ​ (Incorrect)
- m = -1, y = 0 [Image] ​ (Incorrect)
- m = 2, y = 0 [Image] ​ (Incorrect)
- m = 1, y = 6 [Image] ​ (Incorrect)
- m = -1, y = 6 [Image] ​ (Correct)
A: m = -1, y = 6 [Image] ​

Q: Find the slope and the y-intercept of the line 7y + 35 = 0 and sketch its graph.

​
- m = 0, y-intercept is 5 [Image] ​ (Incorrect)
- m = 5, y-intercept is 0 [Image] ​ (Incorrect)
- m = 0, y-intercept is 10 [Image] ​ (Incorrect)
- m = 0, y-intercept is -5 [Image] ​ (Correct)
- m = -5, y-intercept is 0 [Image] ​ (Incorrect)
A: m = 0, y-intercept is -5 [Image] ​

Q: Casey and Mark are running a race at constant speeds. The graph below shows the distance d (in miles) they have traveled since they started the race at time t (in minutes). Which one of the following statements is true?

[Image] [Image]
- Not enough information (Incorrect)
- Mark is running faster than Casey. (Incorrect)
- Casey is running at 0.24 mph, while Mark is running at 0.34 mph. (Incorrect)
- Casey is running at 4.1 mph, while Mark is running at 2.95 mph. (Correct)
- Casey and Mark are both traveling at the same constant speed. (Incorrect)
A: Casey is running at 4.1 mph, while Mark is running at 2.95 mph.

Q: A beanstalk grows at a constant rate. The beanstalk's height (inches) as a function of time (days) is modeled by ​h​  = 3 + 0.2​t​. At what rate is the beanstalk growing?

​
- 3 inches/day (Incorrect)
- 0.2 inches/day (Correct)
- 3.2 inches/day (Incorrect)
- Not enough information (Incorrect)
- 1 inch/day (Incorrect)
A: 0.2 inches/day

Q: Casey and Mark are running a race at constant speeds. After 13 minutes, Casey has traveled 1.35 miles. After 16 minutes, Mark has traveled 1.6 miles. Which of the following statements are true? Check all statements that apply.

​
- Casey's average speed is 8.67 mph.
- Casey is running faster than Mark.
- Mark's average speed is 6.00 mph.
- Casey and Mark are both running at the same constant speed.
- Mark will eventually catch up to Casey if they both continue to run at their constant speed.
A: Casey is running faster than Mark.; Mark's average speed is 6.00 mph.

Q: Which of the following functions are linear? Check all functions that apply.

​
- ​y = [Image]
- ​y = [Image]
- y = [Image]
- y = -5
- ​y = 1 - 6​x​
A: ​y = [Image]; y = -5; ​y = 1 - 6​x​

Q: Write an equation for the line described. Use the simplified form.

Passes through (1, -5) with slope 1
- y = x + 6
- y = x - 4
- y = -x - 6
- y = x - 6
A: y = x - 6

Q: Write an equation for the line described. Use the simplified form.

Passes through (4, 2) with slope - [Image]
- y = - [Image]x - [Image]
- y = - [Image]x + [Image]
- y = - [Image]x + [Image]
- y = - [Image]x - [Image]
A: y = - [Image]x + [Image]

Q: Write an equation for the line described. Use the simplified form.

Passes through (2, -2) and has slope 0
- y = 2
- y = -2
- x = -2
- x = 2
A: y = -2

Q: Write an equation for the line described. Use the simplified form.

Passes through (5, 3) and has no slope
- x = 3
- x = 5
- y = 3
- y = 5
A: x = 5

Q: Write an equation for the line described. Use the simplified form.

Passes through (-3, 7) and (2, -5)
- y = [Image]x - [Image]
- y = [Image]x - [Image]
- y = - [Image]x - [Image]
- y = - [Image]x - [Image]
A: y = - [Image]x - [Image]

Q: Write an equation for the line described. Use the simplified form.

Passes through (7, 0) and (-8, -4)
- y = - [Image]x - 18
- y = - [Image]x - [Image]
- y = [Image]x - 18
- y = [Image]x - [Image]
A: y = [Image]x - [Image]

Q: Write an equation for the line described. Use the simplified form.

Has slope [Image] and y-intercept 7
- y = [Image]x - 7
- y = [Image]x + 7
- y = [Image]x + 7
- y = 7
A: y = [Image]x + 7

Q: Write an equation for the line described. Use the simplified form.

Has y-intercept -5 and x-intercept -3
- y = - [Image]x + 5
- y = - [Image]x - 5
- y = - [Image]x + 5
- y = - [Image]x - 5
A: y = - [Image]x - 5

Q: Write an equation for the line described. Use the simplified form.

Passes through (-3, 10) and is parallel to the line 5x - 6y = -51
- y = - [Image]x + [Image]
- y = [Image]x + 2
- y = - [Image]x - [Image]
- y = [Image]x + [Image]
A: y = [Image]x + [Image]

Q: Write an equation for the line described. Use the simplified form.

Passes through (9, -9) and perpendicular to the line 9x + 4y = 45
- y = [Image]x + 117
- y = - [Image]x - 13
- y = [Image]x - 13
- y = [Image]x
A: y = [Image]x - 13

Q: Find the line's x- and y-intercepts and use this information to graph the line.

x + 3y = 6
- x-intercept = 6, y-intercept = -2 [Image]
- x-intercept = 6, y-intercept = 2 [Image]
- x-intercept = -6, y-intercept = 2 [Image]
- x-intercept = 2, y-intercept = 6 [Image]
A: x-intercept = 6, y-intercept = 2 [Image]

Q: Find the line's x- and y-intercepts and use this information to graph the line.

-4x - 5y = 20
- x-intercept = 5, y-intercept = -4 [Image]
- x-intercept = -5, y-intercept = -4 [Image]
- x-intercept = -4, y-intercept = -5 [Image]
- x-intercept = -5, y-intercept = 4 [Image]
A: x-intercept = -5, y-intercept = -4 [Image]

Q: Find the line's x- and y-intercepts and use this information to graph the line.

x - 4y = -4
- x-intercept = 4, y-intercept = 1 [Image]
- x-intercept = -4, y-intercept = -1 [Image]
- x-intercept = -4, y-intercept = 1 [Image]
- x-intercept = 1, y-intercept = -4 [Image]
A: x-intercept = -4, y-intercept = 1 [Image]

Q: Find the line's x- and y-intercepts and use this information to graph the line.

[Image]x + [Image]y = [Image]
- x-intercept = - [Image], y-intercept = [Image] [Image]
- x-intercept = - [Image], y-intercept = - [Image] [Image]
- x-intercept = [Image], y-intercept = [Image] [Image]
- x-intercept = [Image], y-intercept = - [Image] [Image]
A: x-intercept = [Image], y-intercept = [Image] [Image]

Q: Find the line's x- and y-intercepts and use this information to graph the line.

2.5x - y = 5
- x-intercept = -2, y-intercept = 5 [Image]
- x-intercept = 2, y-intercept = 5 [Image]
- x-intercept = 2, y-intercept = -5 [Image]
- x-intercept = -2, y-intercept = -5 [Image]
A: x-intercept = 2, y-intercept = -5 [Image]