APlot the given ordered pairs to create a scatter plot. The horizontal axis represents laps completed.
BPick two points from the line that you made in Part A and substitute their coordinates into slope formula.
AScatter Plot:
Example Line of Best Fit:
BExample Equation: y=30x Example Conjecture: After walking 15 laps, the number of Calories burned will be equal to about 450.
Practice makes perfect
We are given a table which shows the number of Calories burned when walking laps around a track.
Laps Completed
1
2
3
4
5
6
7
Calories Burned
30
70
80
112
150
170
225
We are asked to construct a scatter plot and draw 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, 70) on a coordinate plane. The horizontal axis will represent the numbers of laps and the vertical axis will represent the number of Calories burned.
In a similar way, we will now graph the other points from the table.
We constructed a scatter plot of the data! Now we will draw a line of best fit. Remember that we should try for the line to be as close to the data points as possible.
The points are very close to the line and a similar number of points is above and below the line. Therefore, this line seems like it represents the data well. 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 best 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 first choose any two points on the line.
The first point that we chose has coordinates x_1= 0 and y_1= 0. The second point has coordinates x_2= 5 and y_2= 150. Let's substitute these values into slope formula.
We found that the slope m is equal to 30. This means that the number of Calories burned increases by 30 per lap.
y=mx+b ⇔ y= 30x+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 0. Finally, we will write an equation of our line of best fit in slope-intercept form
y=30x+b ⇕ y=30x+ 0 ⇕ y=30x
Finally, we will make a conjecture about the number of Calories burned y if someone walks 15 laps x.
To do that, let's substitute x=15 into the equation.
We found that after walking 15 laps, the number of Calories burned will be equal to about 450. Note that if your line of best fit was different, your conjecture will also be different.
