Answer:
[tex] f(x) = -4x - 2 [/tex]
Step-by-step explanation:
To derive the function rule in slope-intercept form, [tex] f(x) = mx + b [/tex], we need to find the slope, m, and the y-intercept, b, of the graph given.
Using two points on the line, (-1, 2) and (0, -2), find slope (m) as shown below:
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 2}{0 -(-1)} = \frac{-4}{1} = -4 [/tex]
m = -4
The line intercepts the y-axis at y = -2, therefore the y-intercept, b, = -2.
Substitute m = -4, and b = -2 into [tex] f(x) = mx + b [/tex].
The function rule in slope-intercept form would be:
[tex] f(x) = -4x +(-2) [/tex]
[tex] f(x) = -4x - 2 [/tex]
