Answer
$\frac{5}{3}x-y=-5$
Work Step by Step
If the line has intercepts $a=-3$ and $b=5$ this means it contains $(-3,0)$ and $(0,5)$ .
We need to find the slope now:
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{5-0}{0-(-3)}=\frac{5}{3}$
Now, with the slope-intercept form, with m=$\frac{5}{3}$ and passing through $(-3,0)$, the equation is:
$y-y_{1}=m\times (x-x_{1})= y-0 = \frac{5}{3}\times (x-(-3))$
$y=\frac{5}{3}\times x +5$
So $\frac{5}{3}x-y=-5$
