Maths-
General
Easy

Question

Mark has $100 gift card to buy apps for his smart phone .Each week he buys one new app for $4.99
a) Write an equation that relates the amount left on the card ,y , over time x.
b) Make a graph of the function

hintHint:

We write the equation in slope intercept form, which is y = mx + c, where m is the slope and c is the y intercept. We are given the slope and the y intercept in the question. Then we make a table of different values of x and y from the equation and plot those points in the xy plane.

The correct answer is: plot its graph


    Step by step solution:
    Let the amount left on the gift card be denoted by y.
    Let the time (in weeks) be denoted by x.
    The initial amount on the gift card = $100
    Amount spent each week = $4.99
    Thus, we can say that
    Rate of change of amount left in the gift card with respect to time (in weeks), m = - 4.99
    The value is negative as the amount is decreasing.
    Initial value, c = 100
    Using the slope intercept form of an equation
    y = mx + c
    We get
    y = -4.99x + 100
    The above equation relates the amount left on the card over time
    Next, we construct a table with different values of x and corresponding values of y.
    Putting x = 0 in the above equation, we will get, y = 100
    Similarly, putting x = 1, in the above equation, we get y = 95.01
    Continuing this way, we have
    For x = 2, we get y = 90.02
    For x = 3, we get y = 85.03
    For x = 4, we get y = 80.04
    Making a table of all these points, we have
    x
    0
    1
    2
    3
    4
    y
    100
    95.01
    90.02
    85.03
    80.04
    Now we plot these points on the graph.

    This is the required graph.

    We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.

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