Find the equation of the line through the points (2, 2) and (4, 10).

FindĀ f(-2) for the following piecewise function.

What is the equation of the line between the points (2, 8) and (3, 2)?

It is the same problem I solved in the other question.

y = mx + b

step 1: Calculate m

m = (y1-y0)/(x1-x0)

P1(2,2) and P0(4,10)

x1=2, x0=4, y1=2, y0=10

m= (2-10)/(2-4) = -8/-2 = 4

step 2: Calculate b

Let's take P1(2,2)

y=2, x=2, m=4

2 = 4 (2) + b

2 = 8 + b

b= 2-8 = -6

Solution: y = 4x -6

If you want to evaluate the function for x=-2

f(x) = 4x - 6

f(-2) = 4(-2) - 6 = -8 - 6 = -14

2) P1(2,8) and P0(3,2)

x1=2, x0=3, y1=8, y0=2

step 1: calculate m

m= (y1-y0)/(x1-x0) = (8-2)/(2-3) = 6/(-1) = -6

step 2: calculate b

let's take the point P1(2,8)

x=2, y=8, m = -6

8=-6(2) + b

8=-12+b

b=8+12 = 20

Solution: y = -6x + 20

f(x) = -6x + 20

f(-2) = -6 (-2) + 20 = 12 + 20 = 32

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