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
(4-5)/(1+2) = -1/3
now you try some.
Can someone tell me if my answers are right and explain how you got each one thank you very much !
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 ***
1. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1).
In this case, the points are (-2, 5) and (1, 4).
Let's substitute the values into the formula:
slope = (4 - 5) / (1 - (-2))
= -1 / 3
Therefore, the slope of the line passing through the given points is -1/3.
The answer is C. -1/3.
2. Given the slope of -5/3, we can use the slope-intercept form of a linear equation, y = mx + b, to find the equation of the line.
Let's take one of the given points and substitute the values into the equation:
(12, 13)
13 = (-5/3)(12) + b
13 = -20 + b
b = 33
Now we have the equation of the line: y = (-5/3)x + 33.
We can check if the other given point satisfies this equation:
(17, 10)
10 = (-5/3)(17) + 33
10 = -85/3 + 33
10 = -85/3 + 99/3
10 = 14/3
Since both points satisfy the equation, the line can pass through (12, 13) and (17, 10).
The answer is A. (12, 13) and (17, 10).
3. To find the value of y, we can use the formula: slope = (y2 - y1) / (x2 - x1).
In this case, the points are (6, y) and (10, 1), with a slope of 1/4.
Let's substitute the values into the formula:
1/4 = (1 - y) / (10 - 6)
1/4 = (1 - y) / 4
1 = 4 - 4y
4y = 3
y = 3/4
Therefore, the value of y is 3/4.
The answer is None of the given options.
4. To find the slope of a line passing through two points, you can use the formula: slope = (y2 - y1) / (x2 - x1).
In this case, the points are (4, 2) and (4, -3).
Let's substitute the values into the formula:
slope = (-3 - 2) / (4 - 4)
= -5 / 0
Since the denominator is zero, the slope is undefined.
The answer is D. Undefined.
5. The rate of change is the ratio of the change in distance to the change in time.
In this case, the car is 500 miles from its destination after 2 hours and 410 miles from its destination after 3.5 hours.
Let's calculate the change in distance and the change in time:
Change in distance = 410 - 500 = -90 miles
Change in time = 3.5 - 2 = 1.5 hours
Now, let's calculate the rate of change:
Rate of change = (change in distance) / (change in time)
= -90 / 1.5
= -60 miles per hour
Therefore, the rate of change is -60 miles per hour.
The answer is None of the given options.