Question

For a ground temperature of 15 degree Celsius, the air temperature (t) at an altitude of 500m (h) is 10 degree Celsius. At 2000 m, the air temperature is -5 degree Celsius. Use the ordered pairs (h,t).
a. Find a linear equation for these data points.
b. Use this linear equation to find the air temperature at 1500m.

Answer 1

y=mx+b

Answer 2

You have been given two ordered pairs: (500,10) and (2000,-5)
Can you find the slope of this line?

Answer 3

No I also need help with that.

Answer 4

Subtract the second numbers of the ordered pairs: 10-(-5)=15
Subtract the first numbers of the ordered pairs: (500-2000)=-1500
Put the first number over the second: 15/-1500 =-1/100
That is the slope.

Answer 5

Now substitute the slope and one of the ordered pairs into y = mx + b and find b. Then you will have the equation of your line.

Answer 6

Can you do that?

Answer 7

im doing it now hang on
please

Answer 8

ok

Answer 9

What did you get for b?

Answer 10

wait, I think I did something wrong lemmy double check.

Answer 11

double check granted.

Answer 12

can you pick either one (15/-1500) or (-1/100) as the x and the y?

Answer 13

-1/100 is m, the slope. For x and y you may use either ordered pair you choose.

Answer 14

I got -15 = (1500)(-1/100) + b

Answer 15

\[10=\frac{-1}{100}(500)+b\]
\[10=-5+b\]
\[15=b\]

Answer 16

Solve for b

Answer 17

oh I see now. Thank you for being patient with me.

Answer 18

\[y=\frac{-1}{100}x+15\]

Answer 19

yw

Answer 20

Now replace x with 1500 to find the temperature at 1500 m