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QMI1500 Assignment 2 Possible Solutions
Question 1
The study shows that the demand (number of units sold) for a new product
is 1 100 units per week when priced at R350, and 850 units per week when
priced at R400. Let 𝑥 represent the price of the product and 𝑦 the demand
per week. Assume that the relationship between the price and demand is
linear and that the demand is dependent on the price. The linear equation
you could use to predict the demand for other prices, is
The linear equation is of the form
𝑦 = 𝑎𝑥 + 𝑏
From the given information, two points can be drawn which are
(𝑥1 ; 𝑦1 ) = (350; 1 100) and (𝑥2 ; 𝑦2 ) = (400; 850)
The slope of this linear equation is given by
𝑦2 − 𝑦1 850 − 1100
𝑆𝑙𝑜𝑝𝑒, 𝑎 = = = −5
𝑥2 − 𝑥1 400 − 350
Replacing 𝑎 with −5, the equation becomes
𝑦 = −5𝑥 + 𝑏
One of the points can be used to find the value of b. Using (400; 850) we have
𝑦 = −5𝑥 + 𝑏
850 = −5(400) + 𝑏
850 = −2 000 + 𝑏
850 + 2 000 = 𝑏 = 2 850
The linear equation is therefore
𝑦 = −5𝑥 + 2 850 [Option 2]
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Questions 2 and 3 are based on the following:
Consider the regression line 𝑌 − 7.52𝑋 + 4.26 = 0, where 𝑌 represents the
expenditure of a company (in millions of Rands) and 𝑋 represents the income
tax generated (in millions of Rands).
Question 2
How much expenditure will be incurred if the company generates income tax
of two million two hundred thousand Rand, i.e. R2,2m?
To be able to calculate the expenditure, 𝑌 when the income tax, 𝑋 = 2.2, we need
to first make 𝑌 the subject of the formula or write the equation in standard form:
𝑌 = 𝑎𝑋 + 𝑏
where 𝑎 = 𝑠𝑙𝑜𝑝𝑒 𝑏 = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
The equation 𝑌 − 7.52𝑋 + 4.26 = 0 becomes
𝑌 = 7.52𝑋 − 4.26
Find 𝑌 when 𝑋 = 2.2
𝑌 = 7.52(2.2) − 4.26 = 12.284 ≈ 12.28
[Option 3]
Question 3
What is the slope and intercept of the line?
The standard equation of the regression line is
𝑌 = 7.52𝑋 − 4.26 ≡ 𝑌 = 𝑎𝑋 + 𝑏
𝑆𝑙𝑜𝑝𝑒, 𝑎 = 7.52 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡, 𝑏 = −4.26
[Option 3]
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Empowering you to conquer your world
Question 4
Study the following scatter plot for variables 𝑥 and 𝑦.
Which one of the following statements is true about this scatter plot?
The scatter plot follows a linear pattern with y decreasing as x increases, representing
a negative relationship between the variables.
Answer: There is a negative linear relationship between 𝑥 and 𝑦.
[Option 2]
Question 5
The line parallel to 𝑦 − 3𝑥 = 5 is
First, the equation is rewritten in standard form 𝑦 = 𝑎𝑥 + 𝑏 to get
𝑦 = 3𝑥 + 5
Parallel lines have the same slope. The line parallel to 𝑦 = 3𝑥 + 5 must also have a
slope of 3 just like the one in Option 1: 𝑦 = 3𝑥 − 1
[Option 1]
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Mr K. Mangwadu: B.Sc (Hon) Civil Engineering III (University of Zimbabwe): +27 83 427 5621 Page 3
Empowering you to conquer your world
QMI1500 Assignment 2 Possible Solutions
Question 1
The study shows that the demand (number of units sold) for a new product
is 1 100 units per week when priced at R350, and 850 units per week when
priced at R400. Let 𝑥 represent the price of the product and 𝑦 the demand
per week. Assume that the relationship between the price and demand is
linear and that the demand is dependent on the price. The linear equation
you could use to predict the demand for other prices, is
The linear equation is of the form
𝑦 = 𝑎𝑥 + 𝑏
From the given information, two points can be drawn which are
(𝑥1 ; 𝑦1 ) = (350; 1 100) and (𝑥2 ; 𝑦2 ) = (400; 850)
The slope of this linear equation is given by
𝑦2 − 𝑦1 850 − 1100
𝑆𝑙𝑜𝑝𝑒, 𝑎 = = = −5
𝑥2 − 𝑥1 400 − 350
Replacing 𝑎 with −5, the equation becomes
𝑦 = −5𝑥 + 𝑏
One of the points can be used to find the value of b. Using (400; 850) we have
𝑦 = −5𝑥 + 𝑏
850 = −5(400) + 𝑏
850 = −2 000 + 𝑏
850 + 2 000 = 𝑏 = 2 850
The linear equation is therefore
𝑦 = −5𝑥 + 2 850 [Option 2]
Providing World Class Tuition Fit for Kings & Queens
Mr K. Mangwadu: B.Sc (Hon) Civil Engineering III (University of Zimbabwe): +27 83 427 5621 Page 1
, ROYAL ACADEMY TUTORS
Empowering you to conquer your world
Questions 2 and 3 are based on the following:
Consider the regression line 𝑌 − 7.52𝑋 + 4.26 = 0, where 𝑌 represents the
expenditure of a company (in millions of Rands) and 𝑋 represents the income
tax generated (in millions of Rands).
Question 2
How much expenditure will be incurred if the company generates income tax
of two million two hundred thousand Rand, i.e. R2,2m?
To be able to calculate the expenditure, 𝑌 when the income tax, 𝑋 = 2.2, we need
to first make 𝑌 the subject of the formula or write the equation in standard form:
𝑌 = 𝑎𝑋 + 𝑏
where 𝑎 = 𝑠𝑙𝑜𝑝𝑒 𝑏 = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
The equation 𝑌 − 7.52𝑋 + 4.26 = 0 becomes
𝑌 = 7.52𝑋 − 4.26
Find 𝑌 when 𝑋 = 2.2
𝑌 = 7.52(2.2) − 4.26 = 12.284 ≈ 12.28
[Option 3]
Question 3
What is the slope and intercept of the line?
The standard equation of the regression line is
𝑌 = 7.52𝑋 − 4.26 ≡ 𝑌 = 𝑎𝑋 + 𝑏
𝑆𝑙𝑜𝑝𝑒, 𝑎 = 7.52 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡, 𝑏 = −4.26
[Option 3]
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, ROYAL ACADEMY TUTORS
Empowering you to conquer your world
Question 4
Study the following scatter plot for variables 𝑥 and 𝑦.
Which one of the following statements is true about this scatter plot?
The scatter plot follows a linear pattern with y decreasing as x increases, representing
a negative relationship between the variables.
Answer: There is a negative linear relationship between 𝑥 and 𝑦.
[Option 2]
Question 5
The line parallel to 𝑦 − 3𝑥 = 5 is
First, the equation is rewritten in standard form 𝑦 = 𝑎𝑥 + 𝑏 to get
𝑦 = 3𝑥 + 5
Parallel lines have the same slope. The line parallel to 𝑦 = 3𝑥 + 5 must also have a
slope of 3 just like the one in Option 1: 𝑦 = 3𝑥 − 1
[Option 1]
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Mr K. Mangwadu: B.Sc (Hon) Civil Engineering III (University of Zimbabwe): +27 83 427 5621 Page 3
