Sunday, 19 July 2015

Key Points 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. 1) M determines is the gradient of the line while C determines the coordinates of the Y intercept. Therefore M and C will determine the position of the line and its gradient
    2) (x1,y1) (x2,y2) it determines where the points are, then line them up.
    3) M determines is the gradient of the line while C determines the coordinates of the Y intercept.

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    1. 1) m determines the gradient of the line while c determines the position of the y-intercept
      2) (x1,y1) (x2,y2) it determines where the points are, then connect the lines and then extend it to the end of the graph
      3) m will change the steepness of the line while c will determine where the the line intercepts the y-axis

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    2. 2) LHS must be = to the RHS . The equation must be the same to determine where the point lies

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  2. 1. m=Gradient
    c=Intercept on y-axis
    2. Calculate the gradient of an imaginary line using the two point and see if the imaginary line is the same as the line in te question.
    3. The larger 'm' is, the steeper the line is. The larger 'c' is, the point where the line intercept at the y-axis is higher.

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    1. 2. Calculate the gradient of an imaginary line using the two point and see if the imaginary line have the same 'm' and 'c' as the line in the question.

      3. The larger the absolute value 'm' is, the steeper the line is. The larger 'c' is, the point where the line intercept at the y-axis is higher.

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    1. 1.y is the coordinate of the line on the y axis and determines where on the y axis the point lies and x is the coordinate on the x axis and determines where on the x axis the point lies
      2.calculate the gradient using the points given and replace the values of x and y to find c. to check if the points are on the line, substitute in the values of x and check with the equation that you just formed.
      3. m is the gradient of the line and c is the point on the y axis that the line cuts through when x=0

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  4. 1. m is the gradient of the line, calculated by the rise over the run of the line and c is the point at which the line cuts the y-intercept.

    2. Joining of the coordinates with a straight, thin line can determine the line, and checking with the equations y = mx + c, to check that all coordinates have the same equations.

    3. m determines the direction of the line. If m is positive, the line goes upwards and if m is negative, the line goes downward. c is the position of one of the coordinates that the line will cut and will determine the centre of the line. The higher the value of m gives a steep line while a lower value of m gives a gentle line.

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  5. 1.m is the gradient of the line while c is the coordinates of the y intercept.m and c will therefore determine the gradient and the position of the line.
    2.if the points of the line lines up and the difference of the lines are always the same and have the same gradient,it is a line.
    3.m is the gradient of the line and c is the coordinates of the y intercept.

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    1. 2. Calculate the gradient of an imaginary line using the two point and see if the imaginary line have the same 'm' and 'c' as the line in the question.

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  6. 1) m determines the gradient of the line while c determines the y-intercept of the line.
    2) calculate the gradient using the 2 points and substitute the values of x and y to find c.
    3) m is the gradient while c is the y-intercept.

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  7. 1. m is the gradient of the slope and c is where the line intercepts the y-axis
    2. We have to use the equation to determine where the line lies
    3. m determines the gradient of the line so, when m is greater the line is steeper. c determines where the line passes through the y-axis

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  8. 1. y = mx + c is [How long y axis is]=[Gradient (amount of slope)[x-intercept]+[y-intercept]
    2. Take two points from the x-axis and y-axis. Take y1 minus y2 divided by x1 minus x2. The first coordinate must follow the coordinates before
    3. The gradient (m) affects how steep the line is. The y-intercept (c) affects how high the line will be.

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  10. 1. y=mx+c c is the point where the line intercepts with the y-axis.
    m is the gradient of the line.
    Fill in x with a random number will find you a point in the line.
    2. Using the equation y=mx+c, fill in the x with one of the 2x of the 2 coordinates and you will find their y.
    Do the same for the other.
    If the y corresponds with they y of the coordinates for both, they are on the line. If not, their not.
    3. c is the point where the line intercepts with the y-axis.
    m is the gradient of the line.

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  11. 1} m is the gradient of the slope while c is where the line intercepts y
    2} You would be able to determine the point if it is on the line through the equation of the line for example y=mx+c replace the x with the x coordinates of the pair of coordinates you were given
    3} m determines the gradient of the line while y determine where the line passes through the y-intercept

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  12. 1. m=gradient on the line
    c= the y intercept
    2.Substitute the values into the equation of the line, If the equation is true, then the point is on the line, if it is false, then that point is not on the line
    3.The larger the value of m, the steeper the line,The larger the value of c the point where the y intercepts is higher
    3.

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    1. m determines the gradient of the line and c is wear the y intercepts

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  13. 1. the value M will be the gradient of the line and it will determine how steep the slope would be with c. The value C will be the point where the line intercepts the Y axis
    2. the coordinates will determine where on the graph will the two points be, then connect them and extend the line to the ends of the graph
    3. M will affect the gradient of the line while Y will determine which point would the line intercept Y and to determine how steep the gradient will be

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  14. 1, M refers to the slope/gradient of the line while C is the interception of the line on the y-axis, therefore they will determine the position of the line
    2.Find the gradient of the line and then replace the values of x and y to find c
    3. m is the gradient whilst c is the interception, so eg, when x = 0, y is unknown therefore cuts through the y-axis

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  15. 1) m determines the gradient, where the line intercepts in the x-Axis and c determines where the line will intercept in the y-axis.
    2) Substitute the values, making both the left and right hand side equal. This is why the equation is y=mx+c
    3)m is the gradient while c is the y intercept.

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  16. 1) m represent the gradient of the line and c represents the y-intercept of the line.
    2) (X1,Y1) (X2,Y2). It represents where the points are and connect the points and extend it.
    3)The greater m is, the steeper the line will be. The greater c is, the higher the point the line cuts through.

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  17. 1) c is the point where the line meets on the y axis
    m is the gradient of the line
    x is the coordinate of a point on the x axis
    y is the coordinate of a point on the y axis

    2)substitude the x in the equation with the x axis of the dot, substitude the y in the equation with the y ais of the dot, if y in the equation is equal to mx+c, the dot is on the line

    3)c is the point where the line intercepts with the y-axis
    m is the gradient of the line

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  18. 1)
    y determines the coordinates of the point on the x axis
    m determines the gradient of the line
    x determines the x intercept
    c determines the y intercept

    2)
    Take the first coordinate 'y' and put it on the left hand side of the linear equation
    Afterwards, take the second coordinate 'mx+c' and put it on the right hand side of the linear equation
    If the equation is balanced, the points do lie on a line

    3)
    m determines the steepness of the line
    c determines the y intercept

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  19. 1.m is the gradient of the line. c is the point where the line intercepts the y-axis.
    2.Put the x coordinate in mx+c then compare the answer with the y coordinates.
    For example, if the coordinates are (5,7) then the equation of the line is 2x+3, then put replace x with 5, then it will become 2(5)+3=13.
    13 and 7 are not equal. So, (5,7) does not lie on the line 2x+3.
    3. m affects the slope of the line. If m is negative, the line slopes downward. If m is positive, the line slopes upward. c affects the point where the line intercepts with the y-axis.

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  20. 1. m is the gradient of the line and c is the y-intercept of the line.
    2. substitute the x and y with the coordinates and if the y=mx+c, the point lies on the line
    3.m affects how steep the line is, and c affects how high the line will be.

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  21. 1. y is the graph, m determines the gradient of the line on the graph and c determines coordinates of the y intercept.
    2. Substitute the values into the line equation using y=mx+c.
    3. c determines the steepness of the line. c determines the place the line intercepts the y axis.

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  22. 1. m is the gradient of the line and c is where the line goes through the y axis.
    2. You can use the coordinates to calculate where the line is. Extend the line until it cannot be extended and see if it lies on the line.
    3. Because m is the gradient. If the gradient increases then the point that the line goes through the y axis, which is c, will increase too.

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  23. 1. y = how far up
    x = how far along
    m = Slope or Gradient (how steep the line is)
    c = the y-intercept (where the line crosses the Y axis)
    2. substitute x and y into the equation for the existing line and the new line, and the equation needs to be the same.
    3. c is the point where the line touches with the y-intercept and m is the gradient of the line.

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  25. 1. m is the gradient of the line. c is the y intercept where the line cuts through the y axis
    2. Substitute the x coordinate in mx+c and compare the value to the y value. If the values are not equal the point does not lie on the line.
    3. m affects the gradient of the line. If the slope in going down, the gradient is negative. If the slope is going up, the gradient is positive. c affects the point which the line intercepts with the y axis.

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