Sunday, 19 July 2015

Key Point from Graphs of Linear Functions

Answer the following in your own words. 

1. Given a function y = mx + c, explain the relationship of the function with the points on the line.

2. Given a pair of coordinates, how would you determine if the point lies on a line?

3. Explain the effects of m and c on the straight line.

33 comments:

  1. This comment has been removed by the author.

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  2. y is the y coordinate, x is the coordinate, m is the gradient and c is the y-intercept

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  3. qn 2, the substitute in the x and y values

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  4. it determines a specific to drawing the gradient

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    1. m is the gradient and shows the steepness of the gradient. c is to show y-intercept so we know where to draw the gradient

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  5. This comment has been removed by the author.

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  6. 1) The points on the line will be determined by the function. eg:m is the gradient, c is the y-intercept. x and y are variables.

    2) Substitute in the value of x and y, evaluate, if the values given make a valid equation, then the point lies on the line.

    3) m is the gradient of the line whilst c is the y-intercept of the line.

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    Replies
    1. x and y are the coordinates of 1 point on the graph

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  7. Q1. Points of the line correspond.
    Q2.Substitute the y and x and if the equation is valid than the point is on the line.
    Q3 M is the gradient and affects the steepness and c is the point at which the line intercepts the y-axis

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    1. Q1 The x coordinate and the y coordinate correspond and together they form the points on the line

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  8. 1. x and y can be change and they represents the values on the x and y axes.

    2. You must substitute the x and y value by putting the coordinates into the function y=mx+c.
    Evaluate the value of y=mx+c
    If the values given makes a valid equation, then the point lies on the line.

    3. m is the gradient / steepness of the line.
    c affects the y-intercept of the line.

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  9. 1. The points on the line corresponds to the function.
    2. Substitute in the values of x and y, then you evaluate, then if the values given make a valid equatuion, then the point lies on the line.
    3. m is the gradient of the line and c is the y intercept of the line

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  10. 1) The points on the line are determined by the functions.

    2) Substitute the values of x and y into the equation and evaluate. If the equation is valid, the point lies on the line.
    3) m is the gradient of the line and c is the y-intercept of the line.

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  11. 1) x and y remain unchanged since they determine how the graph appears. x represents the x axis, whereas y represents the y axis. They change the graph via the value of m and c.
    2) We can determine if the point lies on the line by substituting the values of x and y. Then, if the values given make a valid equation, then we can conclude that the point lies on the line.
    3) The effect of m: The greater its value, the steeper the line will be. Whereas, the lesser its value, the gentler the line will be; The effect of c: It determines where the line intercepts the y-axis. Take for example the value of c is 3, then the line would intercept the y-axis at (0,3).

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  12. 1. Given a function y = mx + c, explain the relationship of the function with the points on the line.
    . x and y represent points on a graph.

    2. Given a pair of coordinates, how would you determine if the point lies on a line?
    . I will first substitute the coordinate of 'x' and 'y' into the equation y=mx+c
    and with the gradient and y-intercept given calculate the final equation and if the result of the equation is valid it means that the points lies on the line.

    3. Explain the effects of m and c on the straight line.
    . 'm' determines the steepness of the line while 'c' determines the y-intercept.

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  13. 1) Points on Line will be determined by the function

    2) Substitute in the value of x and y.

    3) m is the gradient of the line whilst c is the y-intercept of the line.

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  14. 1.The y and x are the values of the line.
    2.I substitute the values of x and y and if the function gives a valid equation,then the point is on the line.
    3.M causes the line to be steeper or gentler.c causes the line to be on the negative or a positive side.

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  15. 1) The points correspond to the function
    2) Substitute, Evaluate, Check if valid
    3) m is gradient, c is y-intercept
    the greater |m| is, the steeper it is
    when m -> infinity, undefined.

    the greater c is, the higher the graph is

    BTW:
    I made a python project some time ago, to check if a point is on a line. This is the source code:

    print("What is the gradient (m in y=mx+c) of the line?")
    m = float(input())
    print("What is the y-intercept (c in y=mx+c) of the line?")
    c = float(input())
    print("What is the x coordinate?")
    x = float(input())
    print("What is the y coordinate?")
    y = float(input())

    if y == m * x + c:
    print("The point is on the line")
    else:
    print("The point in not on the line")

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  16. 1. The points of a line may be determined my the function.x and y are points on a line and they may be substituted with numerical values. m is the gradient of the line and c is the y intercept.

    2. the values of x and y may be substituted in the equation. Upon evaluation, if the equation is valid, the point is on the line

    3.m is the gradient of the line and c is the y intercept.

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  17. 1. The points on the line are determined by its functions.
    2. Substitute the values of x and y into the equation. Evaluate by simplifying the equation. If the values given make a valid equation, then the point lies on the line.
    3. m is the gradient of the line. c is the y-intercept of the line

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  18. 1. The coordinates of the line (x-axis and y-axis) would have to fit into the equation
    2. point:5,13 line:y=2x+3
    13=2(5)+3
    13=10+3
    the point lies on the line
    3. M is the gradient of the line
    C is the y intercept

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    Replies
    1. *x coordinate
      y coordinate
      small letter m and c
      (oh my 天)Mrs Sin

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  19. 1. The x and y values correspond and can be changed
    2. Substitute the x and y values into the equation and if both values make a valid equation, the point lies on the line
    3. m is the gradient and affects the direction that the line is facing and whether it is going upward or downward.
    c is the y-intercept and affects the point in which the line will intersect the y-axis.

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  20. 1. Given a function y = mx + c, explain the relationship of the function with the points on the line.
    The points on the line are affected by the function (i.e. if m is the gradient, then c is the y-intercept. x and y are then the variables. x coordinate corresponds with the y coordinate or vice-versa.
    2. Given a pair of coordinates, how would you determine if the point lies on a line?
    Substitute the value of x and y coordinates into the equation of the line. If the values make a valid equation (fits into the equation), the point lies on the line.
    3. Explain the effects of m and c on the straight line.
    C is the y-intercept and m is the gradient of the line. The line will be parallel to the x-axis, meaning the gradient is 0.

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  21. Answer 1: In y = mx + c, c represents the y-intercept and m is the gradient. In the equation, m and c are defined when doing questions. However, x and y remains as x and y as they can be any number that is a point on the line. Thus, there can be many values of x and y. So, we will just leave it as x and y.]

    Answer 2: First, we have to replace the x and y coordinates with actual values on the line. After that, we need to work it out to find out whether the sum is correct. If the 2 number are the same e.g. 6=6, then the two points lie on the straight line. However, if it is e.g. 8=4, then they are not lying on a straight line.

    Answer 3: On a straight line, c represents the y-intercept where the line passes through on the line axis. m represents the gradient of the line. m affects the 'steepness' of the line, depending on how big or small the gradient is.

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  22. 1. The function is mx + c. "m" is the gradient, "c" is the y-intercept, "x" is the x-coordinate, which can be substituted by a value, "y" is the y-coordinate, which can be substituted by a value. "c" determines which point of the y-axis the line will intercept, "m" determines how steep or gentle the slope of the line is.

    2. Substitute the values of the coordinates of the point into the equation of the line. Evaluate the Right-Hand Side of the equation. After simplifying, if the value of the Left-Hand Side of the equation is equal to the value of the Right-Hand Side of the equation, the point is lying on the line.

    3. "m" is the gradient of the line, "c" is the y-intercept of the line. The value of "m" decides how steep or gentle the slope of the line is. If "m" is positive, the line will point upwards (Left to Right). If "m" is negative, the line will point downwards (Right to Left). The value of "c" decides which point the line will intercept the y-axis at.

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  23. 1) The points on the line are determined by their functions.
    2) To determine the points, substitute the values of x and y. If you get a valid equation then u can tell that the points lie on the line.
    3) m is the gradient of the line, c is the y-intercept of the line.

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  24. 1) The line's points are determined by the function.
    2) Substitute the x and y values
    3) m is the gradient and c is the y intercept

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  25. 1) X and Y affects the position of the lines
    2) Substitute the values of x and y. If the values that you get makes a valid equation, it means the point lies on the line
    3) M is the gradient, so if it is a negative gradient, It will be downwards. C is the y intercept so if its eg -9, the line will intercept at point -9 for the y axis

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