1.
What is the slope of the line containing points (3, 5) and (2, 4)?
Correct Answer
A. 1
Explanation
The slope of a line can be found using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (3, 5) and (2, 4). Plugging these values into the formula, we get (4-5)/(2-3) = -1/-1 = 1. Therefore, the slope of the line is 1.
2.
What is the slope of the line containing points (-2, 3) and (4, -1)?
Correct Answer
B. -2/3
Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates of the two points are (-2, 3) and (4, -1). Plugging these values into the formula, we get (-1 - 3) / (4 - (-2)) = -4 / 6 = -2 / 3. Therefore, the slope of the line is -2/3.
3.
What is the slope of the line containing points (4, 8) and (2, -2)?
Correct Answer
C. 5
4.
When you drive a certain speed, the distance you travel is directly proportional to the time your travel and your speed is the slope of the equation of the line relating your distance and speed. Would the slope of the line be a positive number, negative number, zero or undefined?
Correct Answer
A. Positive
Explanation
The slope of the line would be positive because the question states that the distance traveled is directly proportional to the time and speed. In a direct proportion, as one variable increases, the other variable also increases. Therefore, as the speed increases, the distance traveled also increases, resulting in a positive slope.
5.
What is the slope of the line determined by (3, 4) and (5, 4)?
Correct Answer
A. 0
Explanation
The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the y-coordinates of both points are the same (4), indicating that there is no change in the y-coordinate. Therefore, the slope of the line is 0.
6.
What is the slope of the line determined by the points (4, 3) and (4, 5)?
Correct Answer
B. Undefined
Explanation
The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between any two points on the line. In this case, the x-coordinates of both points are the same, which means there is no change in the x-coordinate. Therefore, the change in x-coordinates is zero. When dividing any number by zero, the result is undefined. Hence, the slope of the line determined by the given points is undefined.
7.
If the x-coordinates stay the same, but the y-coordinates change, what is the slope of the line?
Correct Answer
B. Undefined
Explanation
If the x-coordinates stay the same but the y-coordinates change, it means that the line is vertical. A vertical line has a slope that is undefined because the change in y-coordinates is infinite while the change in x-coordinates is zero. Therefore, the slope of the line is undefined.
8.
If the y-coordinates stay the same and the x-coordinates change, what is the slope of the line?
Correct Answer
A. Zero
Explanation
If the y-coordinates stay the same and the x-coordinates change, it means that the line is horizontal. A horizontal line has a slope of zero because the change in y is always zero regardless of the change in x. Therefore, the slope of the line is zero.
9.
You write an equation to describe the linear relationship between your checking account balance and the number of times you pay your rent, which is $1000 every month. If the rent is the slope of your line, would it be a positive slope, a negative slope, a zero slope, or an undefined slope?
Correct Answer
B. Negative
Explanation
The correct answer is negative. Since the rent is a constant amount that is subtracted from the checking account balance each month, the relationship between the two variables is a negative slope. As the number of times you pay your rent increases, the checking account balance decreases by $1000 each time.
10.
Find the slope of the line containing points (4, 5) and (-1, 3).
Correct Answer
C. 2/5
Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates are (4, 5) and (-1, 3). Plugging these values into the formula, we get (3 - 5) / (-1 - 4) = -2 / -5 = 2/5. Therefore, the slope of the line is 2/5.