Question
Part A
Find the slope of the following graph and choose the correct result.
A
14\frac{1}{4}
4
1
B
13\frac{1}{3}
3
1
C
15\frac{1}{5}
5
1
D
23\frac{2}{3}
3
2
(b)
Part B
Find the slope of the following graph and enter your result in the empty box.
Slope
=
=
Find the slope of the following graph and choose the correct result.
A
14\frac{1}{4}
4
1
B
13\frac{1}{3}
3
1
C
15\frac{1}{5}
5
1
D
23\frac{2}{3}
3
2
(b)
Part B
Find the slope of the following graph and enter your result in the empty box.
Slope
=
=
Answers
GPT-4o mini
To find the slope of a graph, you use the formula:
\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]
where \(\Delta y\) is the change in the y-coordinates and \(\Delta x\) is the change in the x-coordinates between two points on the graph.
### Part A
Let's go through each option to calculate the slope:
#### Option A
- Point: \((1, 14\frac{1}{4})\) or \((1, 14.25)\)
- Point: \((4, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 14.25 = -13.25
\]
\[
\Delta x = 4 - 1 = 3
\]
Now calculate the slope:
\[
\text{slope} = \frac{-13.25}{3} \approx -4.4167
\]
#### Option B
- Point: \((1, 13\frac{1}{3})\) or \((1, 13.33)\)
- Point: \((3, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 13.33 = -12.33
\]
\[
\Delta x = 3 - 1 = 2
\]
Now calculate the slope:
\[
\text{slope} = \frac{-12.33}{2} = -6.165
\]
#### Option C
- Point: \((1, 15\frac{1}{5})\) or \((1, 15.2)\)
- Point: \((5, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 15.2 = -14.2
\]
\[
\Delta x = 5 - 1 = 4
\]
Now calculate the slope:
\[
\text{slope} = \frac{-14.2}{4} = -3.55
\]
#### Option D
- Point: \((2, 23\frac{2}{3})\) or \((2, 23.67)\)
- Point: \((3, 2)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 2 - 23.67 = -21.67
\]
\[
\Delta x = 3 - 2 = 1
\]
Now calculate the slope:
\[
\text{slope} = \frac{-21.67}{1} = -21.67
\]
### Conclusion for Part A
Choose the option with the least steep slope if that is the correct context. Each slope calculated shows negative values indicating a decrease, which is useful in understanding the options you have. You should select the option corresponding to the desired slope.
### Part B
To complete Part B, please provide specific points or a graph for which you need the slope calculated, and I can assist you in finding the slope.
\[
\text{slope} = \frac{\Delta y}{\Delta x}
\]
where \(\Delta y\) is the change in the y-coordinates and \(\Delta x\) is the change in the x-coordinates between two points on the graph.
### Part A
Let's go through each option to calculate the slope:
#### Option A
- Point: \((1, 14\frac{1}{4})\) or \((1, 14.25)\)
- Point: \((4, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 14.25 = -13.25
\]
\[
\Delta x = 4 - 1 = 3
\]
Now calculate the slope:
\[
\text{slope} = \frac{-13.25}{3} \approx -4.4167
\]
#### Option B
- Point: \((1, 13\frac{1}{3})\) or \((1, 13.33)\)
- Point: \((3, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 13.33 = -12.33
\]
\[
\Delta x = 3 - 1 = 2
\]
Now calculate the slope:
\[
\text{slope} = \frac{-12.33}{2} = -6.165
\]
#### Option C
- Point: \((1, 15\frac{1}{5})\) or \((1, 15.2)\)
- Point: \((5, 1)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 1 - 15.2 = -14.2
\]
\[
\Delta x = 5 - 1 = 4
\]
Now calculate the slope:
\[
\text{slope} = \frac{-14.2}{4} = -3.55
\]
#### Option D
- Point: \((2, 23\frac{2}{3})\) or \((2, 23.67)\)
- Point: \((3, 2)\)
Calculate \(\Delta y\) and \(\Delta x\):
\[
\Delta y = 2 - 23.67 = -21.67
\]
\[
\Delta x = 3 - 2 = 1
\]
Now calculate the slope:
\[
\text{slope} = \frac{-21.67}{1} = -21.67
\]
### Conclusion for Part A
Choose the option with the least steep slope if that is the correct context. Each slope calculated shows negative values indicating a decrease, which is useful in understanding the options you have. You should select the option corresponding to the desired slope.
### Part B
To complete Part B, please provide specific points or a graph for which you need the slope calculated, and I can assist you in finding the slope.