Question 1107701: hello! please help:
A loan officer at a bank earns a $100 commission on each of his loans in addition to his $2100 base monthly salary.
(a) Write an equation for the monthly salary M that the loan officer earns if he has l loans a month.
M =
(b) Find the vertical intercept.
(I, M) =
Explain its meaning in this situation. (Include units with your numerical answers.)
If a loan officer makes ----- loans his/her salary will be ----- for the month.
(c) Find the horizontal intercept.
(I, M) =
Explain its meaning in this situation. (Include units with your numerical answers.)
If a loan officer makes loans his/her salary will be ---- for the month. This ----- is is not possible.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A loan officer at a bank earns a $100 commission on each of his loans in addition to his $2100 base monthly salary.
(a) Write an equation for the monthly salary M that the loan officer earns if he has I loans a month.
M = 100 * I + 2100
(b) Find the vertical intercept.
(I, M) = 2100
Explain its meaning in this situation. (Include units with your numerical answers.)
the vertical intercept is the value of M when I = 0.
you solve for the vertical intercept by making I equal to 0 and then solving for M.
M = 100 * I + 2100 becomes M = 100 * 0 + 2100 which becomes M = 0 + 2100 which becomes M = 2100.
this means that the loan officer makes 2100 a month even if he makes zero loans during the month.
(c) Find the horizontal intercept.
the horizontal intercept is the value of I when the value of M is equal to 0.
you solve for the horizontal intercept by making M equal to 0 and then solving for I.
M = 100 * I + 2100 becomes 0 = 100 * I + 2100.
subtract 2100 from both sides of this equation to get -2100 = 100 * I
divide both sides of this equation by 100 to get -2100 / 100 = I
solve for I to get I = -21.
Explain its meaning in this situation. (Include units with your numerical answers.)
this means that the loan office will not make any money during the month if he sells -21 loans for the month.
this is not possible because the number of loans he sells for the month can't be less than 0.
the minimum amount of loans he sells for the month is 0.
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if youi wanted to graph this function, you would set y = M and x = I and you would graph the equation y = 100 * x + 2100.
y represents the monthly income.
x represents the number of sale he makes during the month.
the graph would look like this:
the area of the graph that is not shaded represents the domain and range of the graph.
the domain is all values of x what lead to a possible value of y.
in this case, the value of x that leads to a possible value of y would be the value of x greater than or equal to 0.
x can't be negative because the number of sales made during the month can't be negative.
since your y-intercept occurs when the value of x is less than 0, that is not a possible situation that can occur in reality.
in this case the value of y that results from values of x will be greater than or equal to 2100.
the minimum value of y is 2100 which occurs when zero sales are made.
the value of y can only go up from there.
the coordinate points on the graph are in (x,y) format, which means that the value of x comes first followed by the value of y.
(0,2100) means the value of y is 2100 when the value of x is 0.
(-21,0) means the value of y is 0 when the value of x is -21.
if you substitute (I,M) for (x,y), then:
(0,2100) means the value of M is 2100 when the value of I is 0.
(-21,0) means the value of M is 0 when the value of I is -21.
likewise, on the graph, (20,4100) means the value of y is 4100 when the value of x is 20.
from the equation y = 100 * x + 2100, when x = 20, this equation becomes y 100 * 20 + 2100 which results in y = 2000 + 2100 which results in y = 4100.
substitute I for x and M for y, and you get the value of M is 4100 when the value of I is 20.
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