The equation of the line passing through $(1,11)$ and $(4,5)$ can be expressed in the form \[\frac{x}{a} + \frac{y}{b} = 1.\]Find $a$.
+1164 CPhill answered this one!
Find the slope [ 5 - 11 ] / [ -4 - 1 ] = -6 / -5 = 6 / 5
Write the equation of the line in point-slope
y = ( 6 /5) ( x - 1) + 11
y = (6/5)x - 6/5 + 11
y = (6/5)x - 6/5 + 55/5
y = (6/5)x + 49/5 multiply both sides by 5/49
(5 / 49)y = (6 /49)x + 1
- (6 / 49)x + ( 5/49) y = 1
And we can write this as
x / ( - 49/6) + y / (49 / 5) = 1
a = -49 / 6
The solution is also posted here: http://file-share-drive-folder.firebaseapp.com
