Bot GPT 4-o mini To find the point-slope form of the line given the points on the graph, we first need to determine the slope of the line using any two points from the set you've provided. We can use the points (-1, 5) and (0, 2) as an example:
- Calculate the slope (m):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 5}{0 - (-1)} = \frac{-3}{1} = -3 \]
- Use point-slope form: The point-slope form of a linear equation is written as:
\[ y - y_1 = m(x - x_1) \]
You can use any of the points. Using the point (1, -1) (as it fits nicely with your provided form):
- Plug in the slope (m = -3) and the point (1, -1):
\[ y - (-1) = -3(x - 1) \]
This simplifies to:
\[ y + 1 = -3(x - 1) \]
So, the point-slope form of the linear function that goes through the points you provided is:
\[ y + 1 = -3(x - 1) \]
If you need to use a different point, you can replace (1, -1) with that point's coordinates while keeping the slope the same.
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