How do you find the slope of the secant lines of f(x) = -3x + 2 f(x)=−3x+2 through the points: (-4,(f(-4)) and (1,f(1))?

1 Answer
mason m
Mar 1, 2016

-3−3

Explanation:

Find the points' yy-values by evaluating f(-4)f(−4) and f(1)f(1):

f(-4)=-3(-4)+2=12+2=14f(−4)=−3(−4)+2=12+2=14

f(1)=-3(1)+2=-3+2=-1f(1)=−3(1)+2=−3+2=−1

The two points on the secant line are (-4,14)(−4,14) and (1,-1)(1,−1).

The slope mm can then be found using the slope equation:

m=(Deltay)/(Deltax)=(14-(-1))/(-4-1)=15/(-5)=-3

This should make sense, since f(x) is a line. The secant line, which passes through two points on f(x), will have to be the exact same as f(x)--there's no other way a line can intercept two points.

Since the secant line is identical to f(x), we can tell that they will have the same slope, and the slope of f(x)=-3x+2 is -3.

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