Assume that the number of defective basketballs produced is related by a linear equation to the total number produced. Suppose that 6 defective balls are produced in a lot of 200, and 15 defective balls are produced in a lot of 300.
you have two points: (200,6) and (300,15)
So, just use the two-point form of the line:
y-6 = (9/100)(x-200)
To find the equation that relates the number of defective basketballs produced to the total number produced, we can use the given information to form a system of equations. Let's denote the total number of basketballs produced as "x" and the number of defective basketballs produced as "y".
From the given information, we have two sets of data points:
1) When x = 200, y = 6 (200 balls produced, 6 of them are defective).
2) When x = 300, y = 15 (300 balls produced, 15 of them are defective).
We can now write two equations based on this information:
Equation 1: 6 = m(200) + b (Using the first data point)
Equation 2: 15 = m(300) + b (Using the second data point)
To find the values of "m" and "b" - the slope and y-intercept of the linear equation, we can solve this system of equations.
First, let's multiply both sides of Equation 1 by 100 and rearrange it:
600 = 200m + 100b
Next, let's multiply both sides of Equation 2 by 20 and rearrange it:
300 = 300m + 20b
Now we have a system of equations:
600 = 200m + 100b
300 = 300m + 20b
To simplify the system, we can divide both equations by their common factors:
6 = 2m + b
15 = 3m + b
Subtracting the first equation from the second equation, we get:
15 - 6 = 3m - 2m + b - b
9 = m
Now substitute this value of "m" into either of the original equations. Let's use the first equation:
6 = 2(9) + b
6 = 18 + b
Solving for "b", we get:
b = 6 - 18
b = -12
Therefore, the equation that relates the number of defective basketballs produced (y) to the total number produced (x) is:
y = 9x - 12
Using this equation, you can find the number of defective basketballs produced for any given total number produced.