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?
To find the value of k, we can use the formula for a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
In this case, we have four data points: (2, 6), (4, 12), (6, 18), (8, 24). We can use any two of these points to find the slope, m.
Let's choose the points (2, 6) and (4, 12) to calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (12 - 6) / (4 - 2)
= 6 / 2
= 3
Now that we have the value for m, we can substitute it into the equation y = mx + b using any of the given points. Let's use the point (2, 6):
6 = 3(2) + b
6 = 6 + b
b = 6 - 6
b = 0
Therefore, the equation for the line is y = 3x + 0.
Since the question asks for the value of k, which corresponds to the coefficient of x, we can say that k = 3.
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.