help

The x-intercept refers to when y=0. 

Also, since the x-intercept is -5, then that means one of the legs of the right triangle is 5. 

Using the formula for the area of a triangle, $\frac{5h}{2}=10 \rightarrow 5h=20 \rightarrow h=4$

Now you have 2 points, (-5, 0) and (0, 4) (using (0, -4) also works i think)

Find the slope to be $\boxed{\frac{4}{5}}$

A slight correction for asdf's answer......the second point is  (4, 0)

And the slope of the line is  [ -5 - 0 ] / [ 0 - 4] = -5 / -4 =   5 /4    ....just as asdf found !!!!

Also  (-4, 0)  can't be an alternative solution because this would mean that the line has a negative slope....