Linear Equations Quiz
The question sheet
Reveal any answer as you study-
What is the general form of a linear equation for linear regression?
- y = a/b + x
- y = a + bx
- y = ax + b^2
- y = abx
Reveal answer
Answer: y = a + bx
Source evidence
PDF page 564: Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form: y = a + bx
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In the equation y = a + bx, which variable is the independent variable?
- y
- b
- x
- a
Reveal answer
Answer: x
Source evidence
PDF page 564: where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Another way to think about this equation is a statement of cause and effect. The X variable is the cause and the Y variable is the hypothesized effect. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
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In the cause-and-effect interpretation, which variable is the cause?
- The constant a
- The X variable
- The Y variable
- The constant b
Reveal answer
Answer: The X variable
Source evidence
PDF page 564: where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Another way to think about this equation is a statement of cause and effect. The X variable is the cause and the Y variable is the hypothesized effect. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
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In the equation y = a + bx, y is called the:
- intercept
- slope
- dependent variable
- independent variable
Reveal answer
Answer: dependent variable
Source evidence
PDF page 564: where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Another way to think about this equation is a statement of cause and effect. The X variable is the cause and the Y variable is the hypothesized effect. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
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Which of the following is a linear equation?
- y = 2^x
- y = 3 + 2x
- y = 3/x + 2
- y = 3 + 2x^2
Reveal answer
Answer: y = 3 + 2x
Source evidence
PDF page 564: The following examples are linear equations. y = 3 + 2x y = –0.01 + 1.2x
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The graph of a linear equation of the form y = a + bx is a:
- curve
- straight line
- circle
- parabola
Reveal answer
Answer: straight line
Source evidence
PDF page 564: The graph of a linear equation of the form y = a + bx is a straight line. Any line that is not vertical can be described by this equation.
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Which kind of line CANNOT be described by y = a + bx?
- An upward-sloping line
- A downward-sloping line
- A vertical line
- A horizontal line
Reveal answer
Answer: A vertical line
Source evidence
PDF page 564: The graph of a linear equation of the form y = a + bx is a straight line. Any line that is not vertical can be described by this equation.
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For AWPS, what is the rate charged per hour?
- $15
- $32
- $31.50
- $25
Reveal answer
Answer: $32
Source evidence
PDF page 565: Aaron's Word Processing Service (AWPS) does word processing. The rate for services is $32 per hour plus a $31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to complete the job. Find the equation that expresses the total cost in terms of the number of hours required to complete the job.
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What is the one-time charge for Aaron's Word Processing Service?
- $32
- $31.50
- $25
- $15
Reveal answer
Answer: $31.50
Source evidence
PDF page 565: Aaron's Word Processing Service (AWPS) does word processing. The rate for services is $32 per hour plus a $31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to complete the job. Find the equation that expresses the total cost in terms of the number of hours required to complete the job.
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What equation expresses AWPS total cost in terms of hours x?
- y = 31.50 + 32x
- y = 63.50x
- y = 31.50x
- y = 32 + 31.50x
Reveal answer
Answer: y = 31.50 + 32x
Source evidence
PDF page 565: Solution 13.3 Let x = the number of hours it takes to get the job done. Let y = the total cost to the customer. The $31.50 is a fixed cost. If it takes x hours to complete the job, then (32)(x) is the cost of the word processing only. The total cost is: y = 31.50 + 32x
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In y = a + bx, what does b represent?
- the x value
- the total cost
- the slope
- the y-intercept
Reveal answer
Answer: the slope
Source evidence
PDF page 565: For the linear equation y = a + bx, b = slope and a = y-intercept. From algebra recall that the slope is a number that describes the steepness of a line, and the y-intercept is the y coordinate of the point (0, a) where the line crosses the y-axis. From calculus the slope is the first derivative of the function. For a linear function the slope is dy / dx = b where we can read the mathematical expression as "the change in y (dy) that results from a change in x (dx) = b * dx".
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The y-intercept is the y coordinate of which point?
- (b, 0)
- (0, b)
- (a, 0)
- (0, a)
Reveal answer
Answer: (0, a)
Source evidence
PDF page 565: For the linear equation y = a + bx, b = slope and a = y-intercept. From algebra recall that the slope is a number that describes the steepness of a line, and the y-intercept is the y coordinate of the point (0, a) where the line crosses the y-axis. From calculus the slope is the first derivative of the function. For a linear function the slope is dy / dx = b where we can read the mathematical expression as "the change in y (dy) that results from a change in x (dx) = b * dx".
Introductory Business Statistics
Introductory Business Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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