From University of Utah

Linear and Nonlinear Functions Quiz

12 questions math Grades 9-12

The question sheet

Reveal any answer as you study

01
In y = mx + b, when is the change in variables between two points in proportion?
- Always
- Only when b is not zero
- As slope, regardless of b
- Never for a line
Reveal answer

Answer: As slope, regardless of b

Source evidence
PDF page 63: Interpret the equation y = mx + b as a linear function. Observe that if b is not zero, the variables are not in proportion; however, the change is in the variables between two points are in proportion (hence the idea of slope). 8.F.3
02
According to the evidence, if b is not zero in y = mx + b, then the variables are:
- Not in proportion
- Constant
- In proportion
- Always equal
Reveal answer

Answer: Not in proportion

Source evidence
PDF page 63: Interpret the equation y = mx + b as a linear function. Observe that if b is not zero, the variables are not in proportion; however, the change is in the variables between two points are in proportion (hence the idea of slope). 8.F.3
03
The variables in a linear relation are in proportion only when the graph goes through:
- The y-axis
- The point (0, 0)
- The point (0, b)
- Any point
Reveal answer

Answer: The point (0, 0)

Source evidence
PDF page 63: The characteristic of a proportional relationship is that the quotient y/x, for values in the proportion, is always the same, and we call this the unit rate of y with respect to x. The significant characteristic of a line is this: for any two points P and Q, the ratio of the change in y from P to Q to the change in x from P to Q is a constant, called the rate of change of y with respect to x. This is an important characteristic: the variables in a linear relation are in proportion only when the graph of the relation goes through the point (0, 0). To see this algebraically: if y is a linear function of x; that is y = mx + b, the the quotient y/x, for x , 0 is y b = m + x x which is definitely not constant for b , 0.
04
For y = mx + b, the quotient y/x equals m + b/x, which is:
- Equal to the slope
- Zero
- Not constant for b ≠ 0
- Always constant
Reveal answer

Answer: Not constant for b ≠ 0

Source evidence
PDF page 63: The characteristic of a proportional relationship is that the quotient y/x, for values in the proportion, is always the same, and we call this the unit rate of y with respect to x. The significant characteristic of a line is this: for any two points P and Q, the ratio of the change in y from P to Q to the change in x from P to Q is a constant, called the rate of change of y with respect to x. This is an important characteristic: the variables in a linear relation are in proportion only when the graph of the relation goes through the point (0, 0). To see this algebraically: if y is a linear function of x; that is y = mx + b, the the quotient y/x, for x , 0 is y b = m + x x which is definitely not constant for b , 0.
05
If a line intersects the y-axis at (0, b), its equation is:
- y = mx
- y = b
- x = a
- y = mx + b
Reveal answer

Answer: y = mx + b

Source evidence
PDF page 64: If the line intersects the y-axis in the point (0, b), then the equation of the line is y = mx + b.
06
If a line is horizontal, its slope is zero and its equation is:
- y = mx + b
- y = mx
- x = a
- y = b
Reveal answer

Answer: y = b

Source evidence
PDF page 64: If the line is horizontal, the slope is zero, and the equation of the line is y = b.
07
If a line is vertical, it has no slope and its equation is:
- x = a
- y = b
- y = mx + b
- y = mx
Reveal answer

Answer: x = a

Source evidence
PDF page 64: If the line is vertical, it has no slope, and its equation is x = a.
08
If a line goes through the origin, its equation is y = mx and the values of y are:
- Equal to b
- Nonlinear
- Proportional to x
- Constant
Reveal answer

Answer: Proportional to x

Source evidence
PDF page 64: If the line goes through the origin, the equation of the line is y = mx and the values of y are proportional to the values of x; otherwise said, y/x = m.
09
If a line has slope m and passes through (x0, y0), its equation is:
- y = mx + b
- x = a
- y − y0 = m(x − x0)
- y/x = m
Reveal answer

Answer: y − y0 = m(x − x0)

Source evidence
PDF page 64: If the line has slope m, and the point (x0, y0) is on the line, then the equation of the line is y − y0 = m(x − x0)
10
In the Boston Envelope example, which salary is modeled by a straight line?
- Both salaries
- Neither salary
- Nkutete's salary
- Federico's salary
Reveal answer

Answer: Federico's salary

Source evidence
PDF page 64: The curve modeling Federico’s salary is a straight line, while that for Nkutete is not; neither the table nor the graph of data points showed a tendency for Nkutete’s salary curve to become steeper and steeper. If we calculate with
11
According to the table, Nkutete's rate of change of salary over time:
- Becomes zero
- Stays the same
- Gets larger
- Gets smaller
Reveal answer

Answer: Gets larger

Source evidence
PDF page 65: the table, we can see that the rate of change of Nkutete’s salary gets larger over time; the value of the graph is that it shows us this instantly.
12
Finding a formula giving one variable as a function of another allows us to:
- Make the graph nonlinear
- Predict future pairs of values
- Remove the slope
- Eliminate the domain
Reveal answer

Answer: Predict future pairs of values

Source evidence
PDF page 65: As we continue to study data for two variables, looking for a relation between them, we hope to find a formula that actually exhibits one variable as a function of the other. This will allow for prediction of future pairs of values not on our table. To set the ground for this, we look at a collection of examples represented in various ways: formula, tables or graphs.