Give (f)x=x^2+x find the equation of the secant line passing through (-5,f(-5)) and (1,f(1)). Write your answer in y=mx+b

Question

Give (f)x=x^2+x find the equation of the secant line passing through (-5,f(-5)) and (1,f(1)). Write your answer in y=mx+b

Answer 1

[(f)x should be written as f(x)]

From the problem definition we have two points on the line of the function, namely:

f(-5) = (-5)^2 + (-5) = 25 - 5 = 20, therefore:

(-5, f(-5) = (-5, 20)

and

f(1) = (1)^2 + 1 = 2, therefore:

(1, f(1) = (1, 2)

Given these two points the secant line is the line that passes through them:

Find the slope between the two points:

m = ∇y / ∇x = (2 - 20) / (1 - (-5)) = -18 / 6 = -3

From y = mx + b, using the point at (1,2):

2 = -3*1 + b or

b = 5

Similarly using the point at (-5, 20):

20 = -3 * (-5) + b = 15 + b or

b = 5

So the secant line is:

y = mx + b = -3*x + 5