We know that the line has intercepts (x,0) and (0,y). And the sum of x and y is 5. So we have the first equation: x + y = 5
Using the formula for the slope of a line we have:
m = [tex] \frac{0-y}{x-0} [/tex] = [tex] \frac{-y}{x} [/tex] = 3
Thus, y = -3x
We now have a system of equation. Using substitution,
x -3x = 5
-2x = 5
x = [tex] \frac{-5}{2} [/tex]
Therefore, y = [tex] \frac{15}{2} [/tex]
Substitute to y = mx +b, the equation of the line is
y = 3x + 15/2
