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

An airplanes change in altitude before landing is shown in the table what equation represents this change in altitudePLEASE HELP SOON class=

Respuesta :

Answer:

[tex]y =-4000x+39000[/tex]

Step-by-step explanation:

Minutes (m)    Altitude(a)

1                       35000

2                      31000

3                      27000

4                     23000

Slope : [tex]m =\frac{y_2-y_1}{x_2-x_1}[/tex]  ---A

[tex](x_1,y_1)=(1,35000)[/tex]

[tex](x_2,y_2)=(2,31000)[/tex]

Substitute the values in A

[tex]m =\frac{31000-35000}{2-1}[/tex]

[tex]m =-4000[/tex]

[tex](x_1,y_1)=(3,27000)[/tex]

[tex](x_2,y_2)=(4,23000)[/tex]

Substitute the values in A

[tex]m =\frac{23000-27000}{4-3}[/tex]

[tex]m =-4000[/tex]

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

[tex]y-y_1 =\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex](x_1,y_1)=(1,35000)[/tex]

[tex](x_2,y_2)=(2,31000)[/tex]

[tex]y-3500 =\frac{31000-35000}{2-1}(x-1)[/tex]

[tex]y-3500 =-4000x+4000[/tex]

[tex]y =-4000x+4000+35000[/tex]

[tex]y =-4000x+39000[/tex]

Thus Option D is correct.

The equation represents this change in altitude is [tex]y =-4000x+39000[/tex]

The equation that represents this change in altitude is [tex]\sigma = -4000m +39000[/tex] and this can be determined by using the point-slope form of the line.

Given :

The data is in the table.

Give that at m = 1 min, [tex]\sigma = 35000[/tex] ft and at m = 2min, [tex]\sigma = 31000[/tex] . Then using the point-slope form of the line which is given by:

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]   --- (1)

where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points on the line.

Now, put the value of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in equation (1).

[tex]\dfrac{\sigma-35000}{m-1}=\dfrac{31000-35000}{2-1}[/tex]

[tex]\dfrac{\sigma-35000}{m-1}=\dfrac{-4000}{1}[/tex]

[tex]\sigma-35000={-4000}{(m-1)}[/tex]

[tex]\sigma - 35000=-4000m+4000[/tex]

[tex]\sigma = -4000m +39000[/tex]

The equation that represents this change in altitude is [tex]\sigma = -4000m +39000[/tex] and this can be determined by using the point-slope form of the line.

For more information, refer to the link given below:

https://brainly.com/question/2263981