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

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)

(10-15)/(13-16) = POSITIVE 5/3
try D

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
----------------
(1-y)/(10-6) = 1/4
so
1 - y = 1
y = 0

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
----------------------
denominator is 4-4 = 0
undefined (although actually that is just the vertical line x = 4)

90 miles in 1.5 hours

yes 60 mph

On 3. 0 isn't an answer..

from (6,0)

to (10,1)
is up 1 and right 4
so slope = 1/4
so if 0 is not an answer, you have a typo

1. To find the slope of a line passing through two points, we use the formula:

slope = (change in y-coordinate)/(change in x-coordinate)
In this case, the two points are (-2, 5) and (1, 4).
The change in x-coordinate is 1 - (-2) = 3.
The change in y-coordinate is 4 - 5 = -1.
So, the slope is (-1)/(3) = -1/3.

2. We are given that the slope is -5/3.
To find two points through which this line can pass, we can choose any two points as long as their coordinates satisfy the equation y = mx + c, where m is the slope.
Let's choose the points (16, 15) and (13, 10).
The change in x-coordinate is 13 - 16 = -3.
The change in y-coordinate is 10 - 15 = -5.
So, the slope is (-5)/(-3) = 5/3, which matches the given slope of -5/3.

3. We are given two points (6, y) and (10, 1) that lie on a line with a slope of 1/4.
Using the formula for slope, we can write:
slope = (change in y-coordinate)/(change in x-coordinate)
1/4 = (1 - y)/(10 - 6)
Cross-multiplying, we get:
4(1 - y) = 1(10 - 6)
4 - 4y = 4
-4y = 4 - 4
-4y = 0
Dividing both sides by -4, we get:
y = 0
So, the value of y is 0.

4. To find the slope of a line passing through two points, we use the formula:
slope = (change in y-coordinate)/(change in x-coordinate)
In this case, the two points are (4, 2) and (4, -3).
The change in x-coordinate is 4 - 4 = 0.
Since the change in x-coordinate is zero, we cannot calculate the slope using this formula.
Therefore, the slope is undefined.

5. To find the rate of change, we use the formula:
rate of change = (change in y-coordinate)/(change in x-coordinate)
In this case, the car is 500 miles from its destination after 2 hours, and 410 miles from its destination after 3.5 hours.
The change in x-coordinate is 3.5 - 2 = 1.5.
The change in y-coordinate is 410 - 500 = -90.
So, the rate of change is (-90)/(1.5) = -60.
However, rate of change should be positive in this context, representing the speed of the car.
Therefore, we take the absolute value, which is 60.
Hence, the rate of change is 60 miles per hour.