Question

Can someone help me answer these two questions? I wanna know what's right and wrong. Please correct me if Necessary

for #1 I chose A
and for #2 I chose D

Answer 1

Remember that the general equation of a line is
`y=mx+b`, where:

`m` is the slope, and
`b` is the y-intercept; so to find the y-intercept, solve for
`y` and identify
`b`.
Now, to find the x-intercept, just replace
`y` in your line equation with
`0`, and solve for
`x`
Lets apply those procedures to our two questions:

1. - y-intercept:

`-10x+5y=40`

`5y=10x+40`

`y= (10x+40)/(5)`

`y=2x+8`
Notice that now we have our line equation in the form
`y=mx+b` with
`m=2` and
`b=8`; sine
`b` is the y-intercept, we can conclude that the y-intercept of our equation is 8.

x-intercept:
First, lets replace
`y` with
`0`:

`0=2x+8`
And then, we can solve for
`x` to find our x-intercept:

`2x=-8`

`x= (-8)/(2)`

`x=-4`
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:

`5x+4y=80`

`4y=-5x+80`

`y= (-5x+80)/(4)`

`y=- (5)/(4) x+20`
We can conclude that our y-intercept is 20.

x-intercept:

`0=- (5)/(4) x+20`

`- (5)/(4) x=-20`

`x=( (4)/(5) )(20)`

`x=16`
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.