Finding The Slope Given Two Points

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| By Nrosenstein
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Nrosenstein
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Quizzes Created: 4 | Total Attempts: 4,662
Questions: 13 | Attempts: 121

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Finding The Slope Given Two Points - Quiz


Questions and Answers
  • 1. 

    Find the slope of the line passing through the points (2,5), (2,8).

    Explanation
    The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the x-coordinates of the two given points are the same (both 2), which means the change in x is 0. When the change in x is 0, the slope is undefined because division by zero is undefined in mathematics. Therefore, the slope of the line passing through the points (2,5) and (2,8) is undefined.

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  • 2. 

    Find the slope of the line passing through the points (2,1), (0,1).

    Explanation
    The points (2,1) and (0,1) have the same y-coordinate, which means they lie on a horizontal line. A horizontal line has a slope of 0, as it does not rise or fall in the y-direction. Therefore, the slope of the line passing through these points is 0.

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  • 3. 

    Find the slope of the line passing through the points (5,-1), (-2,-3).

    Explanation
    To find the slope of a line passing through two points, we can use the formula: slope = (y2-y1)/(x2-x1). In this case, the coordinates of the two points are (5,-1) and (-2,-3). Plugging these values into the formula, we get: slope = (-3-(-1))/(-2-5) = (-3+1)/(-2-5) = -2/-7 = 2/7. Therefore, the slope of the line passing through these two points is 2/7.

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  • 4. 

    What is the slope of the line passing through the points (4,2), (8,4)?

    Explanation
    The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4,2) and (8,4). Plugging these values into the formula, we get (4 - 2) / (8 - 4) = 2 / 4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

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  • 5. 

    Find the slope of the line passing through the points (-6,2), (0,-6).

    Explanation
    To find the slope of a line passing through two points, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-6,2) and (0,-6). Using the formula, we can substitute the values: slope = (-6 - 2) / (0 - (-6)) = -8 / 6 = -4 / 3. Therefore, the slope of the line passing through these two points is -4/3.

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  • 6. 

    Find the slope of the line passing through the points (-3,-3), (2,2).

    Explanation
    The slope of a line passing through two points can be found using the formula: slope = (change in y-coordinates)/(change in x-coordinates). In this case, the change in y-coordinates is 2 - (-3) = 5, and the change in x-coordinates is 2 - (-3) = 5. Therefore, the slope of the line passing through the points (-3,-3) and (2,2) is 5/5 = 1.

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  • 7. 

    The slope of the line passing through the points (1,4), (-7,4) is...

    Explanation
    The slope of a line passing through two points can be found using the formula (y2-y1)/(x2-x1). In this case, the y-coordinates of both points are the same, which means that the line is horizontal. When the line is horizontal, the difference in y-coordinates is always 0. Therefore, the slope of the line passing through the given points is 0.

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  • 8. 

    The slope of the line passing through the points (1,9), (-3,5)

    Explanation
    The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (1,9) and (-3,5). Plugging these values into the formula, we get (5 - 9) / (-3 - 1) = -4 / -4 = 1. Therefore, the slope of the line passing through these points is 1.

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  • 9. 

    The slope of the line passing through the points (6,-9), (-3,1)

    Explanation
    The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (6, -9) and (-3, 1). Plugging these values into the formula, we get (-9 - 1) / (6 - (-3)) = -10/9. Therefore, the slope of the line passing through these points is -10/9.

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  • 10. 

    The slope of the line passing through the points (3,9), (-1,7)

    Explanation
    The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula (y₂ - y₁) / (x₂ - x₁). In this case, the points are (3,9) and (-1,7). Plugging the values into the formula, we get (7 - 9) / (-1 - 3) = -2 / -4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

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  • 11. 

    Identify the slope of this equation:  y = 3/5x - 6

    Explanation
    The slope of the equation y = 3/5x - 6 is 3/5. The slope represents the rate at which the y-coordinate changes with respect to the x-coordinate. In this equation, the coefficient of x is 3/5, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3/5. Therefore, the slope of the equation is 3/5.

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  • 12. 

    Identify the y-intercept of the equation:  y = 3/5x - 1

    Explanation
    The y-intercept of an equation represents the point where the line crosses the y-axis. In the given equation, y = 3/5x - 1, the y-intercept is -1. This means that when x is 0, the value of y is -1.

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  • 13. 

    Put this equation into y = mx + b form:  -2x + y = 5

    Explanation
    The given equation, -2x + y = 5, can be rearranged into y = 2x + 5 form by isolating the y variable. By adding 2x to both sides of the equation, we get y = 2x + 5. This equation represents a linear function in slope-intercept form, where the coefficient of x is the slope (2) and the constant term (5) is the y-intercept. Therefore, the correct answer is y = 2x + 5.

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  • Current Version
  • Feb 26, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 14, 2011
    Quiz Created by
    Nrosenstein
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