Remember that the general equation of a line is [tex]y=mx+b[/tex], where:
[tex]m[/tex] is the slope, and [tex]b[/tex] is the y-intercept; so to find the y-intercept, solve for [tex]y[/tex] and identify [tex]b[/tex].
Now, to find the x-intercept, just replace [tex]y[/tex] in your line equation with [tex]0[/tex], and solve for [tex]x[/tex]
Lets apply those procedures to our two questions:
1. - y-intercept:
[tex]-10x+5y=40[/tex]
[tex]5y=10x+40[/tex]
[tex]y= \frac{10x+40}{5} [/tex]
[tex]y=2x+8[/tex]
Notice that now we have our line equation in the form [tex]y=mx+b[/tex] with [tex]m=2[/tex] and [tex]b=8[/tex]; sine [tex]b[/tex] is the y-intercept, we can conclude that the y-intercept of our equation is 8.
x-intercept:
First, lets replace [tex]y[/tex] with [tex]0[/tex]:
[tex]0=2x+8[/tex]
And then, we can solve for [tex]x[/tex] to find our x-intercept:
[tex]2x=-8[/tex]
[tex]x= \frac{-8}{2} [/tex]
[tex]x=-4[/tex]
We can conclude that our x-intercept is -4; thus the correct answer in your list is the fourth one: x-intercept is -4; y-intercept is 8.
2. y-intercept:
[tex]5x+4y=80[/tex]
[tex]4y=-5x+80[/tex]
[tex]y= \frac{-5x+80}{4} [/tex]
[tex]y=- \frac{5}{4} x+20[/tex]
We can conclude that our y-intercept is 20.
x-intercept:
[tex]0=- \frac{5}{4} x+20[/tex]
[tex]- \frac{5}{4} x=-20[/tex]
[tex]x=( \frac{4}{5} )(20)[/tex]
[tex]x=16[/tex]
We can conclude that our x-intercept is 16; thus the correct answer in your list is, once again, the fourth one: x-intercept is 16; y-intercept is 20.
