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

Answer :

Answer:

[tex]F = 1.8C +32[/tex]

[tex]F = 86^{\circ}F[/tex]

Step-by-step explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

[tex](C_1,F_1) = (100,212)[/tex]

[tex](C_2,F_2) = (0,32)[/tex]

Solving (a): Represent as a linear equation

First, we calculate the slope:

[tex]m = \frac{F_2 - F_1}{C_2 - C_1}[/tex]

This gives:

[tex]m = \frac{32 - 212}{0 - 100}[/tex]

[tex]m = \frac{-180}{- 100}[/tex]

[tex]m = 1.8[/tex]

The linear equation is then calculated using:

[tex]F - F_1 = m(C -C_1)[/tex]

Where

[tex](C_1,F_1) = (100,212)[/tex]

[tex]m = 1.8[/tex]

[tex]F - 212 = 1.8(C -100)[/tex]

[tex]F - 212 = 1.8C -180[/tex]

Make F the subject

[tex]F = 1.8C -180+212[/tex]

[tex]F = 1.8C +32[/tex]

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

Substitute 30 for C in [tex]F = 1.8C +32[/tex]

[tex]F = 1.8 * 30 + 32[/tex]

[tex]F = 54 + 32[/tex]

[tex]F = 86[/tex]

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Rewritten by : Jeany

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