APlot the given ordered pairs to create a scatter plot. The horizontal axis should represent the storage amounts in megabytes.
BPick two points that lie the line from Part A. Then, substitute their coordinates into slope formula.
CSubstitute 32 for x into the equation from Part B
AScatter Plot:
Example Line of Best Fit:
BExample Equation: y=2.37x+3 Interpretation of the Slope and Y-intercept: See solution.
CExample Answer: The cost of a flash drive with 32 MB of storage is about 78.84 dollars.
Practice makes perfect
We are given a table which shows the storage amount and cost for flash drives at a local electronics store.
Storage (MB)
2
2
2
2
4
4
4
4
8
8
8
8
8
16
16
16
16
Cost ($)
6.5
12
7
10
9
10
20
23
15
17
20
25
40
23
40
50
80
We are asked to construct a scatter plot and draw a line that best represents the data, which is a line of best fit. To construct a scatter plot, we need to sketch each point from the table. For example, let's sketch the second point from the table ( 2, 12) on a coordinate plane. The horizontal axis will represent storage amounts and the vertical axis will represent the costs of for flash drives.
In a similar way, we will now graph the other points from the table.
We constructed a scatter plot of the data! Now let's draw a line of best fit. Remember that we should try for the line to be as close to the data points as possible.
Most of The points are close to the line and a similar number of points is above and below the line. Therefore, this is a line of best fit. Notice that, if you sketch a different line that is close to the data points, it would also be a correct answer.
In Part A, we drew the following line of fit.
Let's write an equation in slope-intercept form for this line!
y=mx+bIn this equation, m is the slope and b is the y-intercept. To find the slope m, we will choose any two points on the line.
We chose two data points, so that we can identify their coordinates from the given table. The first point has coordinates x_1= 6 and y_1= 20. The second point has coordinates x_2= 22 and y_2= 65. Let's substitute these values into slope formula.
We found that the slope m is equal to 2.37. This means that the cost of a flash drive increases by 2.37 per megabyte of storage.
y=mx+b ⇔ y= 2.37x+b
Now we will find the y-intercept b, which is the y-value when x=0. We can find it on the graph!
We can see that when x=0, the y-value is equal to about 3. Therefore, the y-intercept b is also equal to about 3. This means that a flash drive without any storage would cost about 3 dollars.
y=2.37x+b ⇕ y=2.37x+ 3
We wrote an equation of the line in slope-intercept form!
In Part B, we wrote an equation which approximates the cost y of a flash drive with x megabytes of storage.
y=2.37x+3
We are asked to use this equation to make a conjecture about the cost of a flash drive with a storage capacity of 32 MB. To do that, we will substitute x=32 into the equation.
