1. What is the slope of the line that passes through the points (-2, 5) and (1, 4)?

A. -3
B. -2
C. -1/3
D. 1/3

2. A line has a slope -5/3. Through which two points could this line pass?
A. (12, 13) and (17, 10)
B. (16, 15) and (13, 10)
C. (0, 7) and (3, 10)
D. (11, 13) and (8, 18)

3. The pair of points (6,y) and (10,1) lies on a line with the slope 1/4. What is the value of y?
A. -5
B. -2
C. 2
D. 5

4. What is the slope of the line that passes through the points (4, 2) and (4, -3)?
A. -1
B. 0
C. 1
D. Undefined

5. A car is 500 miles from its destination after 2 hours and 410 miles from its destination after 3.5 hours. What is the rate of change?
A. 1.5 miles per hour
B. 60 miles per hour
C. 90 miles per hour
D. 135 miles per hour

The answers are

C. -1/3
D. (11,13) and (8,18)
B. -2
D. UNDEFINED
B. 60 MILES PER HOUR

thanks for absolutly no help.

1. The slope of the line can be found using the formula (y2 - y1) / (x2 - x1) = (4 - 5) / (1 - (-2)) = -1 / 3. So, the answer is C. -1/3.

2. To find the two points, you can use the formula y = mx + b, where m is the slope. Let's use the point (12, 13) as an example. 13 = (-5/3)*(12) + b. Solving for b, we get b = 13 + (60/3) = 13 + 20 = 33. So, the equation of the line is y = (-5/3)*x + 33. Let's check the options:

A. 13 = (-5/3)*(12) + 33, which is false.
B. 15 = (-5/3)*(16) + 33, which is false.
C. 7 = (-5/3)*(0) + 33, which is true.
D. 13 = (-5/3)*(11) + 33, which is false.

Therefore, the line can pass through points (0, 7) and (3, 10). The answer is C.

3. Again, we can use the formula (y2 - y1) / (x2 - x1) = (1 - y) / (10 - 6) = 1 / 4. Solving for y, we get 1 - y = (10 - 6) / 4 = 4 / 4 = 1. Therefore, y = 1 - 1 = 0. The answer is B. -2.

4. The slope of the line can be found using the formula (y2 - y1) / (x2 - x1) = (-3 - 2) / (4 - 4) = -5 / 0. Division by zero is undefined, so the answer is D. Undefined.

5. The rate of change or the average speed can be found using the formula rate = (change in distance) / (change in time). The change in distance is 410 - 500 = -90 miles and the change in time is 3.5 - 2 = 1.5 hours. So, the rate = (-90) / 1.5 = -60 miles per hour. But since speed cannot be negative, we take the absolute value and the answer is B. 60 miles per hour. Note: I didn't use humor for this question because driving at high speeds is no joke! Safety first! Stay safe on the roads!

To find the slope of a line that passes through two given points (x₁, y₁) and (x₂, y₂), we use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Now let's solve each question step by step:

1. The given points are (-2, 5) and (1, 4). We can use the slope formula:

slope = (4 - 5) / (1 - (-2))
= -1 / 3
= -1/3

Therefore, the slope of the line that passes through the points is -1/3. The correct option is C.

2. The given slope is -5/3. We need to find which pair of points satisfies this slope. We can use the slope formula:

-5/3 = (y₂ - y₁) / (x₂ - x₁)

Let's try each option using the slope formula:

A. (-5/3) = (10 - 13) / (17 - 12) - Incorrect

B. (-5/3) = (10 - 15) / (13 - 16) - Incorrect

C. (-5/3) = (10 - 7) / (3 - 0) - Correct

D. (-5/3) = (18 - 13) / (8 - 11) - Incorrect

The pair of points (0,7) and (3,10) satisfies the slope -5/3. The correct option is C.

3. The given points are (6, y) and (10, 1). The slope is given as 1/4. We can use the slope formula:

1/4 = (1 - y) / (10 - 6)

Simplifying the equation:

1/4 = (1 - y) / 4

Now solve for y:

1 - y = 1
y = 1 - 1
y = 0

Therefore, the value of y is 0. The correct option is none - None of the given options match the value y = 0.

4. The given points are (4, 2) and (4, -3). We can use the slope formula:

slope = (-3 - 2) / (4 - 4)

Since the x-coordinates are the same, the denominator becomes 0:

slope = (-3 - 2) / (0)
= -5 / 0

A slope with a denominator of 0 is undefined. The correct option is D.

5. We have two time-distance pairs: (2, 500) and (3.5, 410). We can use the slope formula:

rate of change = (distance₂ - distance₁) / (time₂ - time₁)

rate of change = (410 - 500) / (3.5 - 2)
= (-90) / (1.5)
= -60

Therefore, the rate of change is -60 miles per hour. The correct option is not provided - None of the given options match the rate of change -60 mph.

slope is change in y divided by the change in x. So,

#1: (4-5)/(1-(-2))
#2: gotta do the division till you find the right pair.
#3: change in y is 1/4 the change in x. So, since x changes by 4, y changes by 1...
#4: since x has not changed, the line is vertical
#5: again, since the rate you want is mi/hr, divide the change in distance by the change in time.
(500-410)mi / (3.5-2.0)hr = 90mi/1.5hr = 60 mi/hr

Great Job Steve, I like that you didn't put only the answer. I needed help with the last one and you really helped.