1. What is the slope of the line that passes through the points (-2,5) and (1,4)?
C: -1/3
2. A line has slope -5/3. Through which two points could this line pass?
D: (11,13), (8,18)
3. The pair of points (6, y) and (10, -1) lie on a line with slope 1/4. What is the value of y?
B: -2
4. What is the slope of a vertical line?
D: Undefined
5. The table below gives the cost per person to rent a fishing charter boat. Find the rate of change given that is it constant. Also, explain what the rate of change means for this situation.
People | Cost $
2 110
3 165
4 220
5 275
D: 55/1
My answers for Linear Functions: Rate of Change and Slope (unit 6, lesson 1)
hi
100% correct thanks!
how do i Find the slope of the line that passes through each pair of points.
(1, 2) and (−3,2)
To find the slope of the line passing through (1, 2) and (−3, 2), we use the slope formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (1, 2) and (x2, y2) = (−3, 2)
Plugging these values into the formula, we get:
m = (2 - 2)/(-3 - 1)
m = 0/-4
m = 0
Therefore, the slope of the line passing through (1, 2) and (−3, 2) is 0.
a person is 100% correct I just took the assessment and got a 100.
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), so we can substitute the coordinates into the formula: Slope = (4 - 5) / (1 - (-2)) = -1/3. Therefore, the slope of the line is -1/3.
2. To find two points through which a line with a given slope could pass, you can choose any two points as long as their coordinates satisfy the slope equation. In this case, the slope is -5/3. Let's say we choose (11,13) and (8,18) as the two points. We can use the slope formula to check if they satisfy the equation: (-5/3) = (18 - 13) / (8 - 11). Simplifying this equation: (-5/3) = 5 / (-3), we can see that the slope equation holds true. Therefore, the line could pass through the points (11,13) and (8,18).
3. We are given that the points (6, y) and (10, -1) lie on a line with a slope of 1/4. Using the slope formula, we can substitute the coordinates into the equation: (1/4) = (-1 - y) / (10 - 6). Simplifying this equation: (1/4) = (-1 - y) / 4, we can see that the numerator and denominator are equal. Therefore, -1 - y = 1, and solving for y, we find that y = -2.
4. A vertical line has an undefined slope. This is because vertical lines are parallel to the y-axis and have no change in x-coordinates. Since the slope formula is based on the change in y divided by the change in x, dividing by zero results in an undefined value for the slope. Therefore, the slope of a vertical line is undefined.
5. To find the rate of change for a given situation, we look for the constant change in one variable for a given change in another variable. In this case, we have a table that gives the cost per person to rent a fishing charter boat. Looking at the table, we can see that for each increase of 1 person, the cost increases by $55. Therefore, the rate of change is $55 for each additional person. This means that for every additional person added to the fishing charter, the cost increases by $55.