Applied exercises: Linear functions

To determine the linear function $t(x):y=m_{t}x+b_t$ for converting the temperature, you first compute the slope $m$ by taking any two points. For example, choose $A(0|32)$ and $B(20|68)$ and compute the slope by taking the difference quotient:

Now determine the $y-$axis intercept $b_t$ by substituting a point, given within the table, into the general function equation. Alternatively, you may read off, at which value $t$ intersects the $y$-axis (which is a fast but unprecise method).

$t(x):y=m_{t}x+b_t$

For example, insert $A$.

$32=1.8\cdot 0+b_t$

Simplify.

$32=b_t\Rightarrow b_t=32$

The formula for calculating Fahrenheit from Celsius is therefore $t(x)=1.8x+32$.