Slope Formula And Rate Of Change

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| By Simonedeitch

Simonedeitch

Community Contributor

Quizzes Created: 6 | Total Attempts: 4,843

Questions: 8 | Attempts: 266 | Updated: Mar 16, 2023

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Otherwise known as gradient, the slope is a graphical method of calculating the direction and steepness of a line. Through it, different mathematical concepts are achieved. Find out what you know about slope formula and the rate of change below.

Questions and Answers

1.

What is the best description of the slope of a horizontal line?
- A.
  
  It is positive
- B.
  
  It is negative
- C.
  
  It is 0
- D.
  
  It is undefined
Correct Answer
C. It is 0

Explanation
The best description of the slope of a horizontal line is that it is 0. This is because a horizontal line has a constant y-coordinate and does not change in the x-direction. Therefore, there is no change in the y-coordinate for any change in the x-coordinate, resulting in a slope of 0.

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2.

What is the best description of the slope of a vertical line
- A.
  
  It is positive
- B.
  
  It is negative
- C.
  
  It is 0
- D.
  
  It is undefined
Correct Answer
D. It is undefined

Explanation
The slope of a vertical line is undefined because a vertical line is perfectly vertical and does not have any horizontal change. In other words, the line does not have a defined rise over run, which is the basis for calculating slope. Therefore, the slope of a vertical line cannot be determined.

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3.

What is the best description of the slope of the line shown in the graph?
- A.
  
  It is positive.
- B.
  
  It is negative
- C.
  
  It is 0
- D.
  
  It is undefined
Correct Answer
B. It is negative

Explanation
The slope of a line represents the steepness or incline of the line. In this case, since the correct answer is "It is negative," it means that the line is sloping downwards from left to right. This indicates that as the x-values increase, the corresponding y-values decrease.

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4.

Find the slope of the line that passes through the pair of points. ( -2, 1 ) ( -5, 1 )
- A.
  
  Undefined
- B.
  
  0
- C.
- D.
Correct Answer
B. 0

Explanation
The slope of a line is calculated using the formula (change in y)/(change in x). In this case, the y-coordinates of both points are the same, which means there is no change in y. Therefore, the slope is 0.

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5.

Find the slope of the line that passes through the pair of points. (–3, –2), (5, 4)
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
The slope of a line passing through two points can be found using the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the first point are (-3, -2) and the coordinates of the second point are (5, 4). Plugging these values into the formula, we get (4 - (-2)) / (5 - (-3)) = 6 / 8 = 3/4. Therefore, the slope of the line passing through these two points is 3/4.

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6.

What is the slope of the line?
- A.
  
  -1
- B.
  
  -2
- C.
  
  2
- D.
  
  -3
Correct Answer
B. -2

Explanation
The slope of a line represents the rate of change between any two points on the line. In this case, the slope is -2. This means that for every 1 unit increase in the x-direction, the y-coordinate decreases by 2 units. Similarly, for every 1 unit decrease in the x-direction, the y-coordinate increases by 2 units. The negative sign indicates that the line is sloping downwards from left to right.

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7.

What is the slope of the line? (The points shown are (4,4) (6,7) (8,10). Remember: you only need 2 points to make a line! )
- A.
  
  -3/2
- B.
  
  3
- C.
  
  2/3
- D.
  
  3/2
Correct Answer
D. 3/2

Explanation
The slope of a line can be found using the formula (change in y) / (change in x). In this case, we can choose any two points to calculate the slope. Let's choose the points (4,4) and (6,7). The change in y is 7-4 = 3, and the change in x is 6-4 = 2. Therefore, the slope is 3/2.

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8.

What is the y-intercept of the line y = -3x - 7? (*remember in class we started by changing the y= to standard form then looked for the intercepts using the cover up method.)
- A.
  
  3
- B.
  
  7
- C.
  
  -7
- D.
  
  -3
Correct Answer
C. -7

Explanation
In class we have changed this to standard form then done the cover up method to find the intercepts.

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Current Version
Mar 16, 2023

Quiz Edited by
ProProfs Editorial Team
Nov 01, 2013

Quiz Created by
Simonedeitch

Slope Formula And Rate Of Change

What is the best description of the slope of a horizontal line?

What is the best description of the slope of a vertical line

What is the best description of the slope of the line shown in the graph?

Find the slope of the line that passes through the pair of points. ( -2, 1 ) ( -5, 1 )

Find the slope of the line that passes through the pair of points. (–3, –2), (5, 4)

What is the slope of the line?

What is the slope of the line? (The points shown are (4,4) (6,7) (8,10). Remember: you only need 2 points to make a line! )

What is the y-intercept of the line y = -3x - 7? (*remember in class we started by changing the y= to standard form then looked for the intercepts using the cover up method.)