Slope Question

Question

Assume that the number of defective basketballs produced is related by a linear equation to the total number produced. Suppose that 12 defective balls are produced in a lot of 375, and 20 defective balls are produced in a lot of 550.
Find the number of defective balls produced in a lot of 775 balls.

Answer 1

The number of defective basketballs depends on how many basketballs produced are produced.  This is because if there are no basketballs being produced, then you don't have any defective ones, being that no such basketball exists.

 

Let x = number of balls produced

Let y = number of defective balls

 

 

A linear function is in the form    y=mx+b  , where m is slope and b is y-intercept.

 

We are given two points:

 

Point 1 = (12, 375)

Point 2 = (20, 550)

 

 

Use these points to find the slope.

 

m = (y₂ - y₁) / (x₂ - x₁)

 

m = (550 - 375) / (20 - 12)

 

m = 175 / 8

 

m = 21.875

 

 

So far, the function is              y = 21.875x + b

 

 

Next, plug in the values of the point (12, 375) into this equation to find b.

 

 

375 = 21.875(12) + b

 

375 = 262.50 + b

 

112.50 = b

 

 

The function that represents this relationship is

 

y = 21.875x + 112.50

 

 

 

To find the number of defective balls produced in a lot of 775 balls, evaluate y when  x=775.