BPick two points that lie the line from Part A. Then, substitute their coordinates into slope formula.
CCalculate the number of years between 1999 and 2025 and substitute it into the equation from Part B.
AScatter Plot:
Example Line of Best Fit:
BExample Equation: y=0.04X+0.85 Interpretation of the Slope and Y-intercept: See solution.
CExample Conjecture: in the year 2025 apples will cost 1.85 dollars per pound.
Practice makes perfect
We are given a table which shows the cost per pound of apples for several years
Years Since 1999
1
2
3
4
5
6
7
8
9
10
11
Cost ($)
0.92
0.87
0.95
0.98
1.04
1.07
1.12
1.12
1.32
1.18
1.22
We are asked to construct a scatter plot and draw a line that best represents the data. 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, 0.87) on a coordinate plane. The horizontal axis will represent years somce 1999 and the vertical axis will represent cost per pound of apples.
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 straight line that best represents the data. Remember that we should try for the line to be as close to the data points as possible.
Note that this is only an example of a line of best fit. Other lines that are close to the data points would also be correct.
In Part A, we chose 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.
The first point has coordinates x_1= 4 and y_1= 1.0. The second point has coordinates x_2= 9 and y_2= 1.2. Let's substitute these values into slope formula.
We found that the slope m is equal to 0.04. This means that the price for one pound of apples increases by 0.04 dollars every year.
y=mx+b ⇔ y= 0.04x+b
The y-intercept b is the y-value when x=0. We can find it on the graph. Let's do it!
We can see that the y-intercept b is equal to about 0.85. This means that the cost per pound of apples in 1999 was equal to about 0.85 dollars.
y=0.04x+b ⇕ y=0.04+ 0.85
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 pound of apples x years after the year 1999.
y=0.04x+0.85We are asked to use this equation to make a conjecture about the cost of apples in the year 2025. To do that, we first need to calculate the number of years x between the years 1999 and 2025.
x=2025-1999 ⇔ x=26
Now we can substitute x=26 into the equation from Part B to estimate the cost per pound of apples in 2025.
