Question
The graph represents one side of the roof of a building.
The slope of the line is
The slope of the line is
Answers
GPT-4o
To determine the slope of the line on a graph, you need to identify two points on the line and then use the formula for slope:
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Here are the steps to follow:
1. **Identify Two Points:** Find two exact points on the line. These points should preferably be where the line crosses grid lines for easier calculation (e.g., points like (x1, y1) and (x2, y2)).
2. **Calculate the Difference in y-coordinates (\( \Delta y \))**: Subtract the y-coordinate of the first point from the y-coordinate of the second point.
3. **Calculate the Difference in x-coordinates (\( \Delta x \))**: Subtract the x-coordinate of the first point from the x-coordinate of the second point.
4. **Compute the Slope:** Divide the difference in y-coordinates by the difference in x-coordinates using the formula above.
For example, if the two points identified on the line are (2, 3) and (5, 7):
1. \((x_1, y_1) = (2, 3)\)
2. \((x_2, y_2) = (5, 7)\)
Then, compute the slope as follows:
\[ \Delta y = y_2 - y_1 = 7 - 3 = 4 \]
\[ \Delta x = x_2 - x_1 = 5 - 2 = 3 \]
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{4}{3} \]
Thus, the slope of the line is \(\frac{4}{3}\).
If you provide specific points or a graph, I can give a more precise answer based on those details.
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Here are the steps to follow:
1. **Identify Two Points:** Find two exact points on the line. These points should preferably be where the line crosses grid lines for easier calculation (e.g., points like (x1, y1) and (x2, y2)).
2. **Calculate the Difference in y-coordinates (\( \Delta y \))**: Subtract the y-coordinate of the first point from the y-coordinate of the second point.
3. **Calculate the Difference in x-coordinates (\( \Delta x \))**: Subtract the x-coordinate of the first point from the x-coordinate of the second point.
4. **Compute the Slope:** Divide the difference in y-coordinates by the difference in x-coordinates using the formula above.
For example, if the two points identified on the line are (2, 3) and (5, 7):
1. \((x_1, y_1) = (2, 3)\)
2. \((x_2, y_2) = (5, 7)\)
Then, compute the slope as follows:
\[ \Delta y = y_2 - y_1 = 7 - 3 = 4 \]
\[ \Delta x = x_2 - x_1 = 5 - 2 = 3 \]
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{4}{3} \]
Thus, the slope of the line is \(\frac{4}{3}\).
If you provide specific points or a graph, I can give a more precise answer based on those details.