A carpenter is building a fence in his backyard. He needs to purchase lumber for the fence. Four data points : (2, 6), (4, 12), (6, 18), (8, 24) what is the value of k?

Answer 1

The data points suggest that there is a linear relationship between the amount of lumber purchased (y) and the length of the fence (x). We can use the equation of a straight line (y = mx + b) to find the value of k.

First, we need to find the slope (m) of the line. We can use any two points to do this:

m = (y2 - y1) / (x2 - x1)
m = (12 - 6) / (4 - 2)
m = 6 / 2
m = 3

Now that we know the slope, we can use any of the data points to find the y-intercept (b) and the value of k:

y = mx + b
6 = 3(2) + b
b = 0

Therefore, the equation for the amount of lumber purchased (y) in terms of the length of the fence (x) is:

y = 3x

The value of k is 3.