Please help!! secant question

Question

a) Find the slope of the secant to the graph of f(x)=x^2-4x-30 between the points where x=-2 and x=1

b) Determine an algebraic expression that represents the slope of any secant

line that passes through (8,2) and (x,x^2-4x-30)

thanks for any help possible!!

Answer 1

The secant to the graph is just a line passing through two points on the graph. In order to calculate the slope of that line you need to know the y coordinates of the points where x = -2 and x = 1.

Then the slope will be given by: (f(-2) - f(1))/ (-2 - 1) , i.e. change in y over change in x.I will let you determine the function values at the two points.

Part b is the same idea. The slope for the line joining points (8,2) and some other point on the graph will be given by: m = (f(x) - 2)/ (x - 8). You can replace f(x) in the preceding with x²-4x-30 and then simplify the numerator.

Check out this graph which not only calculates the slope of the secant line, but also displays the graph of the secant line (with an equation written in point-slope form).

https://www.desmos.com/calculator/rvevc4zg0f