To find the slope of a line that crosses the points [tex]\((-4, 4)\)[/tex] and [tex]\( (2, -5) \)[/tex], we use the formula for the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the coordinates [tex]\((x_1, y_1) = (-4, 4)\)[/tex] and [tex]\((x_2, y_2) = ( 2, -5)\)[/tex], we can substitute these into the formula:
[tex]\[ m = \frac{-5 - 4}{2 - (-4)} \][/tex]
First, simplify both the numerator and the denominator:
[tex]\[ \text{Numerator: } -5 - 4 = -9 \][/tex]
[tex]\[ \text{Denominator: } 2 - (-4) = 2 + 4 = 6 \][/tex]
Now, substitute these simplified values back into the slope formula:
[tex]\[ m = \frac{-9}{6} \][/tex]
This fraction can be simplified further. Since both [tex]\(-9\)[/tex] and [tex]\(6\)[/tex] can be divided by [tex]\(3\)[/tex], we get:
[tex]\[ m = \frac{-9 \div 3}{6 \div 3} = \frac{-3}{2} \][/tex]
Therefore, the slope of the line through these points is:
[tex]\[ m = -\frac{3}{2} \][/tex]
None of the given answer choices ([tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{3}{2}\)[/tex], [tex]\(-\frac{2}{3}\)[/tex]) match [tex]\(-\frac{3}{2}\)[/tex].
Thus, there might be a typo or an issue with the multiple-choice answers provided. Based on the calculation, the correct slope is [tex]\(-\frac{3}{2}\)[/tex].
