Mathematics, 13.10.2019 02:00 amberlynnwallac7808

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?

the value of motorbikes decrease each year after purchase. the scatter plot shows the v

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Answer from: oneicyahdaley10

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.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is