Maths-
General
Easy

Question

The table shows the relationship between time and cost. Show that the relationship is linear, and then find the equation for the relationship.

hintHint:

A linear equation is of the form , where m and c are constants.
Slope of a line is m=equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
We are asked to shown that the relation is linear and find a linear equation for the data.

The correct answer is: We are asked to shown that the relation is linear and find a linear equation for the data.


    ANSWER:
    Step 1 of 3:
    Plot the points on a graph,



    The points on the scatter plot forms a straight line.
    Thus, the data of time and cost are linear.
    Step 2 of 3:
    The equation of a linear equation is of the form y equals m x plus c, where .m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction end cell row blank row blank row blank end table
    table attributes columnalign right columnspacing 0em end attributes row cell m equals fraction numerator 60 minus 40 over denominator 10 minus 5 end fraction end cell row blank row blank end table

    table attributes columnalign right columnspacing 0em end attributes row cell m equals 20 over 5 end cell row blank end table
    m equals 4
    Step 3 of 3:
    Slope,
    The equation is . To find the value of , substitute the point in the equation.
    Thus, we have:

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 4 x plus c end cell row blank row blank row blank row blank end table

    table attributes columnalign right columnspacing 0em end attributes row cell 40 equals 4 left parenthesis 5 right parenthesis plus c end cell row blank row blank row blank end table

    table attributes columnalign right columnspacing 0em end attributes row cell 40 equals 20 plus c end cell row blank row blank end table
    table attributes columnalign right columnspacing 0em end attributes row cell 40 minus 20 equals c end cell row cell 20 equals c end cell end table

    Hence, the required equation is .y equals 4 x plus 20
     

    A linear equation is of the form , where m and c are constants.
    Slope of a line is m=equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
    We are asked to shown that the relation is linear and find a linear equation for the data.

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