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This quiz tests the work covered in the lecture on linear functions and corresponds to Section 12.4 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).
There is a great applet at http://www.univie.ac.at/future.media/moe/galerie/geom2/geom2.html which gets you to work out the equations of 5 planes. Make sure you rotate the planes so that you can see where they cut the axes. You need to do some calculations to find the equations.

There are more web quizzes at Wiley, select Sections 4 and 5. This quiz has 14 questions on both this topic and the next.

Question 1

a)		(3,-2,-1) is a point on the plane.		b)		The slope of the plane in the direction is 3.
c)		The slope of the plane in the direction is 3		d)		The slope of the plane in the direction is -2.
e)		The slope of the plane in the direction is -2.

 

There is at least one mistake.
For example, choice (a) should be false.

Substitute and into the equation and we get so (3,-2,-1) is not on the plane.

There is at least one mistake.
For example, choice (b) should be false.

The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is -2.

There is at least one mistake.
For example, choice (c) should be true.

The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is 3.

There is at least one mistake.
For example, choice (d) should be true.

The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is -2.

There is at least one mistake.
For example, choice (e) should be false.

The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is 3.

Your answers are correct

1. False. Substitute and into the equation and we get so (3,-2,-1) is not on the plane.
2. False. The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is -2.
3. True. The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is 3.
4. True. The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is -2.
5. False. The slope of the plane in the direction is the coefficient of when the equation of the plane is written in this form, so the slope is 3.

Question 2

The following table contains the values of a linear function.

	1	2
1	4	2
2	7	?

Which of the following is the missing value and the equation of the plane, respectively?

a)		4 and		b)		4 and
c)		5 and		d)		5 and

 

Not correct. Choice (a) is false.

Try again, the values are decreasing by 2 and the values are increasing by 3.

Not correct. Choice (b) is false.

Try again, you have the correct values for the slopes in the and directions but you have not calculated the missing value correctly.

Not correct. Choice (c) is false.

Try again, you have calculated the missing value correctly but you do not have the correct equation of the plane.

Your answer is correct.

The values are increasing by 3 and the values are decreasing by 2 so the missing number is 5 and the equation is We find by substituting one of the points into the equation.
so the equation is It is always a good idea to check another point satisfies this equation as well. ( and from the table which gives 2= 3-4+3 in the equation, which is true)

Question 3

a)				b)
c)				d)

 

Your answer is correct.

and we substitute and into the equation to find

We could also solve and we will get the same result.

Not correct. Choice (b) is false.

Try again, you may have used instead of

Not correct. Choice (c) is false.

Try again, the slope in the direction is the coefficient of and the slope in the direction is the coefficient of

Not correct. Choice (d) is false.

Try again, you have not used the correct form for the equation of the plane.

Question 4

Consider the table below.

	1	2	4
1	1	3	7
2	4	6	10
4	10	12	16

Which one of the following statements is correct.

a)		The table of values does not represent a linear function.
b)		The table of values represents the linear function
c)		The table of values represents the linear function
d)		The table of values represents the linear function

 

Not correct. Choice (a) is false.

Try again, it does. Note that the and values are not evenly spaced.

Not correct. Choice (b) is false.

Try again, you have not calculated the slopes correctly.

Your answer is correct.

You have noted that the and values are not evenly spaced and that the slope in the direction is 3 and the slope in the direction is 2 so the equation is

Not correct. Choice (d) is false.

Try again, look carefully at the order of the variables.