Question 1155260
x = number of units of product A per week.
y = number of units of product B per week.
product A requires 4 hours per unit and product B requires 6 hours per unit.
total hours available per week = 120.
equation becomes 4x + 6y = 120
convert this to slope intercept form as follows:
subtract 4x from both sides of the equation and arrange the right side of the equation in descending order of degree to get:
6y = -4x + 120
divide both sides of this equation by 6 to get:
y = -4/6 * x + 120 / 6
simplify to get:
y = -2/3 * x + 20
questions to answer are:


a) Determine the equation which states the total time expended for producing these two products equals 120 hours per week


4x + 6y = 120


this equation says that 4 hours are expended for every unit of product A and 6 hours are expended for every unit of product B.
x = the number of units for product A.
y = the number of units for product B.


b) Rewrite the equation in the slope intercept from and identify the slope and y intercept


y = -2/3 * x + 20


the general form of the slope intercept form of the equation is y = mx + b
m is the slope and b is the y-intercept.
m = -2/3
y-intercept = 20



c) Interpret the meaning of the slope and y intercept in this application. 


the y-intercept is the value of y when x = 0.
when x = 0, the formula becomes y = 20.
this is saying that, if no units of product A are produced, and 120 hours a week are still required, than 20 units of product B are produced.


the slope tells you the change in the number of units of y for every change in the number of units for x.
a slope of -2/3 is equivalent to (-2/3) / 1.
this says that, when x increases by 1, y decreases by 2/3.
this translates to the change in the number of units of product B for every change in the number of units of product A.
it says that, when the number of units of product A increases by 1, the number of units of product B decreases by 2/3.



it might be useful to show you what happens via a graph.
the graph is shown below.


<img src = "http://theo.x10hosting.com/2020/040401.jpg" alt="$$$" >


you can see that, when x = 0, y = 20.
this means that no units are produced for product A and 20 units are produced for product B.


you can see that, when x = 6, y = 16 and when x = 12, y = 12.


y = -2/3 * x + 20 is the equation.
when x = 6, y = -2/3 * 6 + 20 which becomes y = -4 + 20 which becomes y = 16.
when x = 12, y = -2/3 * 12 + 20 which becomes y = -8 + 20 which becomes y = 12.


the change in x from 6 to 12 is 6.
the change in y from 16 to 12 is -4.
the change in y divided by the change in x is -4/6 which simplifies to -2/3.
that's your slope.