Question
Find the slope of the line graphed below. Use whatever method you would like. Describe what method you have used in complete sentences.
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GPT-4o mini
To find the slope of a line, you can use the formula for the slope (m), which is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
This formula calculates the change in y (vertical change) divided by the change in x (horizontal change) between two points on the line.
Assuming we have the coordinates of two points on the line, let's denote them as Point 1 (x₁, y₁) and Point 2 (x₂, y₂).
1. **Select Two Points**: Choose two distinct points on the line. For example, let's say those points are (2, 3) and (4, 7).
2. **Identify the Coordinates**: From these points, we identify:
- Point 1: (2, 3) — here, x₁ = 2 and y₁ = 3
- Point 2: (4, 7) — here, x₂ = 4 and y₂ = 7
3. **Apply the Slope Formula**: Plugging these values into the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2
\]
4. **Interpret the Result**: The slope of the line is 2. This means that for every increase of 1 unit in the horizontal direction (x-axis), the line rises by 2 units vertically (y-axis).
In summary, I used the slope formula based on two specific points on the line, calculated the differences in the y-coordinates and x-coordinates, and determined that the slope of the line is 2.
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
This formula calculates the change in y (vertical change) divided by the change in x (horizontal change) between two points on the line.
Assuming we have the coordinates of two points on the line, let's denote them as Point 1 (x₁, y₁) and Point 2 (x₂, y₂).
1. **Select Two Points**: Choose two distinct points on the line. For example, let's say those points are (2, 3) and (4, 7).
2. **Identify the Coordinates**: From these points, we identify:
- Point 1: (2, 3) — here, x₁ = 2 and y₁ = 3
- Point 2: (4, 7) — here, x₂ = 4 and y₂ = 7
3. **Apply the Slope Formula**: Plugging these values into the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2
\]
4. **Interpret the Result**: The slope of the line is 2. This means that for every increase of 1 unit in the horizontal direction (x-axis), the line rises by 2 units vertically (y-axis).
In summary, I used the slope formula based on two specific points on the line, calculated the differences in the y-coordinates and x-coordinates, and determined that the slope of the line is 2.
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