To find the slope of the line that passes through the points [tex]\( (2, -8) \)[/tex] and [tex]\( (-4, 4) \)[/tex], you can use the slope formula for 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]
Here, the coordinates are given as:
[tex]\[ (x_1, y_1) = (2, -8) \][/tex]
[tex]\[ (x_2, y_2) = (-4, 4) \][/tex]
Step 1: Substitute the given points into the slope formula.
[tex]\[ m = \frac{4 - (-8)}{-4 - 2} \][/tex]
Step 2: Simplify the numerator:
[tex]\[ 4 - (-8) = 4 + 8 = 12 \][/tex]
Step 3: Simplify the denominator:
[tex]\[ -4 - 2 = -6 \][/tex]
Step 4: Divide the results from Step 2 and Step 3:
[tex]\[ m = \frac{12}{-6} = -2 \][/tex]
Therefore, the slope of the line containing the points [tex]\( (2, -8) \)[/tex] and [tex]\( (-4, 4) \)[/tex] is [tex]\( -2 \)[/tex].
