secant line

A secant line is a straight line so it will have an equation of the form y = m*x + c where m and c are constants.

 

To find the constants first substitute the given values of x into f(x) to find the corresponding values of y

y₃ =  3^3 + 2*3 - 1 or  y₃ =  32

y₅ = 5^3 + 2*5 -1  or  y₅ = 134

 

Now use these values in the equation for the straight line

32 = m*3 + c                 (1)

134 = m*5 + c               (2)

 

Subtract (1) from (2)

102 = 2m so m = 51

 

Put this back into (1)

32 = 51*3 + c

32 = 153 + c

c = 32 - 153 or c = -121

 

So the equation of the secant line is y = 51x - 121