To determine the slope of the line that passes through the points \((4, -1)\) and \((-1, 4)\), we can use the formula for the slope of a line when given two points. The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's assign the coordinates to our variables:
- \((x_1, y_1) = (4, -1)\)
- \((x_2, y_2) = (-1, 4)\)
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{4 - (-1)}{-1 - 4} \][/tex]
First, simplify the numerator \(4 - (-1)\):
[tex]\[ 4 - (-1) = 4 + 1 = 5 \][/tex]
Next, simplify the denominator \(-1 - 4\):
[tex]\[ -1 - 4 = -5 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ m = \frac{5}{-5} = -1 \][/tex]
Thus, the slope of the line that contains the points \((4, -1)\) and \((-1, 4)\) is \(-1\).
The correct answer is B. -1.
