Question
Calculate the slope of the line based on the two points in the graph leave the answer in simplest fraction form, if it applies. If the slope is undefined , enter a value of 100. The point starts at (-4,5) and ends at (8,-1)
Answers
GPT-4o mini
To calculate the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points are \((-4, 5)\) and \((8, -1)\):
- \(x_1 = -4\)
- \(y_1 = 5\)
- \(x_2 = 8\)
- \(y_2 = -1\)
Now plug these values into the slope formula:
\[
m = \frac{-1 - 5}{8 - (-4)} = \frac{-1 - 5}{8 + 4} = \frac{-6}{12}
\]
Simplifying that fraction:
\[
m = \frac{-6}{12} = \frac{-1}{2}
\]
Thus, the slope of the line is:
\[
\boxed{-\frac{1}{2}}
\]
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points are \((-4, 5)\) and \((8, -1)\):
- \(x_1 = -4\)
- \(y_1 = 5\)
- \(x_2 = 8\)
- \(y_2 = -1\)
Now plug these values into the slope formula:
\[
m = \frac{-1 - 5}{8 - (-4)} = \frac{-1 - 5}{8 + 4} = \frac{-6}{12}
\]
Simplifying that fraction:
\[
m = \frac{-6}{12} = \frac{-1}{2}
\]
Thus, the slope of the line is:
\[
\boxed{-\frac{1}{2}}
\]