The manager of a company made the graph below to show the value of a piece of office equipment after each of the 7 years following its purchase.
The graph titled value of equipment shows value on y-axis and time on x-axis. There are dots at (1, 7), (2, 6.5), (3, 6.4), (4, 4), (5, 2.5), (6, 2), and (7, 0.5).
Match the statement with the correct answer
Column A
1.
The slope of the line of best fit:
The slope of the line of best fit
2.
The y-intercept of the line of best fit:
The y-intercept of the line of best fit
3.
The graph of the line of best fit:
The graph of the line of best fit
4.
The correlation of the line of best fit:
The correlation of the line of best fit
5.
The equation for the line of best fit.:
The equation for the line of best fit.
Column B
Column B
a.Strong, positive trend
b.-1
c.Weak, negative trend
d.5
e.Weak, positive trend
f.Strong, negative trend
g.y = -x + 8
h.+1
i.y = 8x + 1
j.(0,8)
k.y = -8x + 1
l.
m.y = x + 8
n.y = 8x - 1
o.
The scatter plot titled value of equipment shows value in thousands of dollars from 0 to 10 and time in years from 0 to 10. The points on the scatter plot are (1, 7), (2, 6.5), (4, 4), (5, 2.5), (6, 2), (7, 0.5)
1. The slope of the line of best fit: -1
2. The y-intercept of the line of best fit: 8
3. The graph of the line of best fit: y = -x + 8
4. The correlation of the line of best fit: Weak, negative trend
5. The equation for the line of best fit: y = -x + 8
Note: There are no options in Column B for statements 11-15.
Column A Column B
1. The slope of the line of best fit: l. y = -x + 8
2. The y-intercept of the line of best fit: j. (0,8)
3. The graph of the line of best fit: o. The scatter plot titled value of equipment shows value in thousands of dollars from 0 to 10 and time in years from 0 to 10. The points on the scatter plot are (1, 7), (2, 6.5), (4, 4), (5, 2.5), (6, 2), (7, 0.5)
4. The correlation of the line of best fit: e. Weak, positive trend
5. The equation for the line of best fit: l. y = -x + 8
Let's match the statements in Column A with the correct answer in Column B:
1. The slope of the line of best fit: g. -1
2. The y-intercept of the line of best fit: j. (0,8)
3. The graph of the line of best fit: m. y = x + 8
4. The correlation of the line of best fit: e. Weak, positive trend
5. The equation for the line of best fit: i. y = 8x + 1
To determine the answers in Column B, we need to analyze the given scatter plot titled "value of equipment" with the points (1, 7), (2, 6.5), (3, 6.4), (4, 4), (5, 2.5), (6, 2), and (7, 0.5).
1. The slope of the line of best fit:
To find the slope of the line of best fit, we can calculate the change in y divided by the change in x using any two points:
Slope = (Change in y) / (Change in x).
Let's take the points (1, 7) and (7, 0.5) from the graph:
Slope = (0.5 - 7) / (7 - 1) = -6.5 / 6 = -1.08 (approximately).
Therefore, the slope of the line of best fit is approximately -1.08.
Answer: b. -1
2. The y-intercept of the line of best fit:
The y-intercept is the value of y when x equals zero. Looking at the scatter plot, we can observe that when x equals zero, y equals 8. Therefore, the y-intercept of the line of best fit is 8.
Answer: j. (0, 8)
3. The graph of the line of best fit:
The line of best fit represents the trend in the data points. Since the slope is negative, the line will have a descending trend. Passing through the y-intercept (0, 8), the line will start at this point and move downward. Visually, the line will slant downward from left to right.
Answer: k. y = -8x + 1
4. The correlation of the line of best fit:
To determine the correlation of the line of best fit, we need to assess the strength and direction of the relationship. Based on the scatter plot, we observe a weak negative trend, meaning that as time increases, the value of the equipment decreases, but the relationship is not very strong. Therefore, the correlation is weak and negative.
Answer: c. Weak, negative trend
5. The equation for the line of best fit:
Using the slope-intercept form of a line, which is y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the values we obtained earlier: m = -1 and b = 8. Plugging these values into the equation, we get:
y = -1x + 8, which can be simplified as y = -x + 8.
Answer: g. y = -x + 8