Question - Determining Slope of a Linear Function from Given Points
Solution:
The question is asking to find the slope of the graph of a linear function $$ f(x) $$ given two points on the line: $$ f(-2) = 8 $$ and $$ f(4) = -2 $$.The slope of a line is given by the change in y-values divided by the change in x-values. Let's denote the points as $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$, where:$$ x_1 = -2 $$, $$ y_1 = f(-2) = 8 $$$$ x_2 = 4 $$, $$ y_2 = f(4) = -2 $$The slope $$ m $$ is calculated as follows:$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$Substitute the given values to find the slope:$$ m = \frac{-2 - 8}{4 - (-2)} $$$$ m = \frac{-10}{6} $$Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:$$ m = \frac{-10/2}{6/2} $$$$ m = \frac{-5}{3} $$So, the slope of the graph of $$ f(x) $$ is $$ -\frac{5}{3} $$, which corresponds to option A.
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