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
Hint:
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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a) Graph the ordered pairs from the table
b) Is the relation a function ? Explain.
In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.
