Question

An airplane's change in altitude before landing is shown in the table. what equation represents this change in altitude?PLEASE HELP SOON

Answer 1

Answer:

$y =-4000x+39000$

Step-by-step explanation:

Minutes (m)    Altitude(a)

1                       35000

2                      31000

3                      27000

4                     23000

Slope : $m =\frac{y_2-y_1}{x_2-x_1}$  ---A

$(x_1,y_1)=(1,35000)$

$(x_2,y_2)=(2,31000)$

Substitute the values in A

$m =\frac{31000-35000}{2-1}$

$m =-4000$

$(x_1,y_1)=(3,27000)$

$(x_2,y_2)=(4,23000)$

Substitute the values in A

$m =\frac{23000-27000}{4-3}$

$m =-4000$

Since the slopes are same.

Thus the given table represents the linear function.

Now we will use two point slope form top obtain the required equation

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

$(x_1,y_1)=(1,35000)$

$(x_2,y_2)=(2,31000)$

$y-3500 =\frac{31000-35000}{2-1}(x-1)$

$y-3500 =-4000x+4000$

$y =-4000x+4000+35000$

$y =-4000x+39000$

Thus Option D is correct.

The equation represents this change in altitude is $y =-4000x+39000$

Answer 2

Answer:

A. $a=-4000m+35,000$  

Step-by-step explanation:

We have been given a table that represents the altitude of an airplane with passing minutes.

Since we know that equation of a line in slope-intercept form is: $y=mx+b$, where, m = Slope of the line and b = y-intercept.

To find the equation of line we will have to the slope of our given line using values from table.

$m=\frac{y_2-y_1}{x_2-x_1}$, where,

$y_2-y_1$ = Change in two y-coordinates.

$x_2-x_1$ = Change in the corresponding x-coordinates.

Upon substituting the coordinates of point (1, 35000) and (2, 31000) we will get our slope as:

$m=\frac{31000-35000}{2-1}$

$m=\frac{-4000}{1}=-4000$

Now let us find y-intercept of our given line by substituting m=-4000 and the coordinates of point (1, 35000) in slope intercept form of equation.

$31000=-4000*1+b$

$31000=-4000+b$

$31000+4000=-4000+4000+b$

$35000=b$

Upon substituting the value of slope and y-intercept the equation of line will be:

$a=-4000m+35,000$

Therefore, the equation representing the change in altitude a after m minutes is $a=-4000m+35,000$ and option A is the correct choice.