Question

HELP!! 

The value of motorbikes decrease each year after purchase. The scatter plot shows the value of the bike (in thousands) over the number of years from first purchase.

(a) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.

(b) Based on the linear model, predict the initial value of a motorbike, Day 0. Approximately how much does it decrease per year?

Answer 1

A. Slope intercept: y= (-8/9)x+10
B. Intially it would have cosaround $9000 but each year it decreases on the chart by -2/3

Answer 2

Answer (a):

Given scatter plot has a line of best fit which passes through two points (1,9) and (8,3)

So we can use those points to find the equation of line shown by the scatter plot.

Let's find the slope first using slope formula

$slope = m =\frac{y_2-y_1}{x_2-x_1}=\frac{3-9}{8-1}=\frac{-6}{7}$

Now plug the value of slope and any point from above two points say (1,9) into point slope formula

$y-y_1=m(x-x_1)$

$y-9=\frac{-6}{7}(x-1)$

$y-9=\frac{-6}{7}x+\frac{6}{7}$

$y=\frac{-6}{7}x+\frac{6}{7}+9$

$y=\frac{-6}{7}x+\frac{6}{7}+9*\frac{7}{7}$

$y=\frac{-6}{7}x+\frac{6}{7}+\frac{63}{7}$

$y=\frac{-6}{7}x+\frac{69}{7}$

Hence required equation of line in slope intercept form is $y=\frac{-6}{7}x+\frac{69}{7}$

Answer (b):

Based on the linear model, we need to predict the initial value of a motorbike, Day 0. To find that we just plug x=0 into obtained equation.

$y=\frac{-6}{7}x+\frac{69}{7}$

$y=\frac{-6}{7}*0+\frac{69}{7}$

$y=\frac{69}{7}$

Hence initial value of motarbike is $\frac{69}{7}$ thousand which is approx 9857 motarbikes.

we found that slope m= -6/7

that indicates number of motarbikes decreases by 6/7 thousand per year or 857 bikes per year.