Find the equation of the line with sum of intercepts is 5 and slope is 3

Question

I am having trouble finding a formula that connects the two and can produce an answer. Anyone know how this is done? I tried y=mx+b, m=3, and b=5-a. But I don't know what to do next or did I even start right.

Answer 1

Try using the intercept form of a line. Assume $x$-intercept to be $a$ and $y$-intercept to be $b$. Then equation of line is given by

$$\frac xa+\frac yb=1.$$ Which implies $$bx+ay=ab$$

So slope of line is: $-\frac ba=3$

Also, you have- $$a+b=5.$$ All that remains is to solve these two equations.

Answer 2

The slope is $3$ so $y = 3x + b$. The intercepts are found when $x = 0$ or $y = 0$, so when $x = 0, y = b$, and when $y = 0, 0 = 3x + b \implies x = -b/3$. Hence $b + (-b/3) = 5$ and you can continue from here.