Determining Slope of a Linear Function from Given Points
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.
