Exercise 1 Page 728

We are asked to number, and then perform the steps in the correct order to write an equation for the line of best fit for the given scatter plot.

When we draw the line of best fit, we usually do it by hand. While doing so, we need to make sure that the line is as close to the data points as possible. Let's do it!

This is Step 1 to our solution.

1. Draw the line.

5. Now, we have a line and we want to write its equation. We are going to write it in slope-intercept form. Here m is the slope and b is the y-intercept of the line. y=mx+b To write the equation we will need two points on the line. These may or not may be the data points. We are also going to highlight them.

   

   This is Step 2 of the process.

   1. Draw the line.
   2. Choose two points.
   Let's now remember the Slope Formula. m = y_2-y_1/x_2-x_1 If we substitute the coordinates of the two points into this formula, we will get the slope of our line m. Let's do it then!
   m = y_2-y_1/x_2-x_1

   SubstitutePoints

   Substitute ( 1,39) & ( 6,44)

   m = 44- 39/6- 1

   SubTerms

   Subtract terms

   m = 5/5

   CalcQuot

   Calculate quotient

   m = 1
   The slope of the line is 1. We completed the third step.
   1. Draw the line.
   2. Choose two points.
   3. Find the slope.

   Now we want to find the y-intercept. This means we need to look for a point where the line crosses the y-axis.

   

   The y-intercept is 38 because the line crosses the y-axis at point (0,38). This was Step 4.

   1. Draw the line.
   2. Choose two points.
   3. Find the slope.
   4. Find the y-intercept.

   We can now substitute the found values into the line equation and simplify. y = 1x+ 38 ⇓ y =x+ 38 Here is the final equation of the line. We can summarize our steps.

   1. Draw the line.
   2. Choose two points.
   3. Find the slope.
   4. Find the y-intercept.
   5. Write the equation in y=mx+b form.

   Note that this is just an example answer. The final results depend on both the line of best fit that we drew and the points that we chose to find the slope.