Question

Water boils at 100LaTeX: ^\circ∘ Celsius or 212LaTeX: ^\circ∘ Fahrenheit. Water freezes at 0LaTeX: ^\circ∘ Celsius or 32LaTeX: ^\circ∘ Fahrenheit. If the weather forecaster says it will be 30LaTeX: ^\circ∘ Celsius today, write and solve a linear equation to find what Fahrenheit temperature this is.

Answer 1

person above me is wrong

Answer 2

`F = 1.8C +32`

`F = 86^(\circ)F`

Explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

`(C_1,F_1) = (100,212)`

`(C_2,F_2) = (0,32)`

Solving (a): Represent as a linear equation

First, we calculate the slope:

`m = (F_2 - F_1)/(C_2 - C_1)`

This gives:

`m = (32 - 212)/(0 - 100)`

`m = (-180)/(- 100)`

`m = 1.8`

The linear equation is then calculated using:

`F - F_1 = m(C -C_1)`

Where

`(C_1,F_1) = (100,212)`

`m = 1.8`

`F - 212 = 1.8(C -100)`

`F - 212 = 1.8C -180`

Make F the subject

`F = 1.8C -180+212`

`F = 1.8C +32`

Solving (b): The value of F when C = 30

Substitute 30 for C in
`F = 1.8C +32`

`F = 1.8 * 30 + 32`

`F = 54 + 32`

`F = 86`