a Choose two convenient points that represent the data well. Recall the forms of a linear equation.
B
b Use the equation found in Part A.
A
aExample Equation: y = - 2.5x+10
B
b It should be around 12.5 inches.
Practice makes perfect
a We are given the graph shown below describing the data collected from an ice sculpture. We need to find the line of best fit.
Recall that the line of best fit does not necessarily go through the data points. We can use two convenient points as long as they represent the behavior of the data well. In the graph below we used (4,0) and (0,10).
Now, to find its equation let's recall the slope-intercept form of a line.
y=mx +b
Here m is the slope of the line and b is the y-intercept. From the chosen points we can see that the y-intercept will be b=10. Now, let's use the chosen points and the Slope Formula.
m=y_2-y_1/x_2-x_1,
With (x_1, y_1) and (x_2,y_2) as two known points, we can find the slope.
Knowing the slope and the y-intercept, we can write the equation for the line of best fit. In this case it would be y = - 2.5x+10. Notice that this is an example answer, as we could have chosen any two points as long as the line they define represents the data well.
b Based on our equation found in Part A, we need to find the height of the sculpture 1 hour before he started recording. For this, we just need to substitute x=- 1 in the equation y = - 2.5x+10.
We found that the height of the sculpture was around 12.5 inches at that time. Take note — the equation is just an example, so this answer is not the only possible answer. However, even using different lines of best fit we should get a result close to 12.5 inches for the height of the sculpture one hour before.
