Interpretation of Slope: The machine produces 5 objects in four minutes.
C75 objects
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=mxHere, 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= 5/4xLet'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!
