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.
1 answer