Question

Question #92ade

Answer 1

`2x+5y=16`

Explanation:

The line `2x+5y=1` can be rewritten as `y=-2/5x+1/5`, which has a slope of `-2/5`.

The line `x-4y=8` has `x`-intercept `(8,0)`, found by letting `y=0` and solving for `x`.

Now we need to write the equation of the line with slope `-2/5`, so it's parallel to `2x+5y=1` passing through `(8,0)`, to satisfy the `x`-intercept requirement.

I like to start with point-slope form: `y-y_0=m(x-x_0)`:

`y-0=-2/5(x-8)`

That's an equation of the line and you could stop there, but I'm thinking we should rewrite it to match the form of the givens.

`y-0=-2/5(x-8)\rightarrow y=-2/5(x-8)`

multiply both sides by 5:

`5y=-2(x-8)`

distribute the `-2`:

`5y=-2x+16`

Add `2x` to both sides:

`2x+5y=16`

and that should be our answer!