Exercise 6 Page 157

Practice makes perfect

We know that the number y objects a machine produces is proportional to the time x in minutes that the machine runs. We want to write an equation that represents a production of five objects in four minutes. To do so, remember that when two quantities are proportional, the relationship can be represented by the following equation. y=mx

Here, m is the constant of proportionality. The graph of this equation is a line with a slope m that passes through the origin. The slope is a ratio used to compare how a variable changes in relation to another variable. m= Change iny/Change in x In our case, the change in y is equal to 5 objects and the change in x is 4 minutes. Then, the slope is m= 54. Now that we know the slope we can substitute it into the proportional relationship. y= 5/4x

Recall the equation obtained in Part A. y= 5/4x

Let's graph this linear equation by using a table of values. We will replace x with 1, 2, and 3 to find the value of y.

x	y=5/4x	y
1	y=5/4( 1)	1.25
2	y=5/4( 2)	2.5
3	y=5/4( 3)	3.75

The value of x and its corresponding value of y represents an ordered pair that can be plotted in a coordinate plane. Let's plot the ordered pairs and draw a line through the points.

We know that the slope of the line is equal to 54. This means that the machine produces 5 objects in four minutes.

We can calculate the number of objects produced in one hour by remembering that one hour is equal to 60 minutes. 1 hour = 60 minutes Now, we will substitute x= 60 into the equation obtained in Part A. Let's do it!

y= 5/4x

Substitute

x= 60

y= 5/4* 60

MoveRightFacToNum

a/c* b = a* b/c

y=5 * 60/4

Multiply

y=300/4

CalcQuot

Calculate quotient

y=75