Question

(giving 100 points) What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.


x y

4 3

6 4

8 9

11 12

13 17



A: y = 1.560x - 4.105

B: y = -4.105x + 1.560

C: y = 4.105x - 1.560

D: y = -1.560x + 4.105

please hurry

Answer 1

Answer:

Slope-intercept form of a linear equation:  $y=mx+b$

where:

• $m$ is the slope
• $b$ is the y-intercept

To determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.

From inspection of the data, we can see that as x increases, y increases.  Therefore, the slope of the equation will be positive.

(If the y-values decrease as the x-values increase, then the slope would be negative).  

Therefore, we can immediately discount answer options B and D as they have negative slopes.

The x and y values are not very far away from each other.  The options given for the slope are either 1.560 or 4.105.  If the slope was 4.105, we would expect to see values of y that were further away from the x-values.

Therefore, the line of best fit is:

A:  y = 1.560x - 4.105

To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).

Choose 2 points on the line of best fit:  (4, 2) and (11, 13)

Use the slope formula with these points to calculate the approximate slope:

$\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57$

Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.