Question

How do you solve it?

Answer 1

At heart we're being asked for a line through two points,

`(40^\circ \textrm{ C}, 355 \textrm { m/s}) \quad \textrm{and} \quad (49^\circ \textrm{ C}, 360 \textrm { m/s})`

In general the line through (a,b) and (c,d) is

`(y-b)(c-a)=(x-a)(d-b)`

Check that you understand why both (a,b) and (c,d) are on this line.

Here our indepedent variable, instead of x, is T, temperature. Our dependent variable is v, velocity. Substituting,

`(v - 355)(49 - 40) = (T - 40)(360 - 355)`

`9(v - 355) = 5(T - 40)`

`v-355 = \frac 5 9 T - (200)/(9)`

`v= \frac 5 9 T - (200)/(9) + 355`

`v= \frac 5 9 T + (2995)/(9)`

That's our answer; let's check it.

When T=40, v = (5/9)40 + (2995/9) = 355 good

When T=49, v= (5/9)49 + (2995/9) = 360 good