Question 100763
We are given:
{{{10C = 50F}}}
{{{40C = 104F}}}
We can assume we have a grid of C (the x-axis) and F (the y-axis).
So these correspondences can be viewed as xy pairs that define points in the plane: (10,50) and (40,104).
Finding the slope of the line, we have:
{{{m=rise/run = (y2 - y1)/(x2 - x1) = (104-50)/(40-10) = 54/30 = 27/15 = 9/5}}}
The general equation for a line is y = mx + b, so
{{{y = (9/5)x + b}}}
And, looking back we notice that when x=10, y=50. So we can substitute:
{{{50 = (9/5)10 + b}}}
{{{50 = 18 + b}}}, so
{{{b = 32}}}, which is the y-intercept.
Now the equation is
{{{y = (9/5)x + 32}}}, which is perhaps more familiar by substituting F for y (meaning degrees Farenheit) and C for x (meaning Celsius).
{{{F = (9/5)C + 32}}}.