Question

If (k, 5) lies on the line with equation 3x-y =-8, what is the value of k?

Show work and explain please

Answer 1

`k=-1`

Explanation:

`"since "(k,5)" lies on the line then it satisfies the equation"`

`"substitute into the equation and solve for k"`

`"that is "x=k" and "y=5`

`rArr3k-5=-8`

`"add 5 to both sides"`

`3kcancel(-5)cancel(+5)=-8+5`

`rArr3k=-3`

`"divide both sides by 3"`

`(cancel(3) k)/cancel(3)=(-3)/3`

`rArrk=-1`

Answer 2

`k=-1`

Explanation:

First, you need to make the equation `3x-y=-8` to the form `y=mx+b`

`3x-y=-8`

`-y=-8-3x`
`y=(-8-3x)/-1`
`y=8+3x`

Now, there are multiple ways you could solve this:

First way is to plug in 5 as the y value in this equation and solve for x.
`y=8+3x`
`5=8+3x`
`-3=3x`
`-1=x`

Second way is to graph this and find out.
The graph should look like this:

graph{8+3x [-10, 10, -5, 5]}
Im portant things ot remember: 8 is the y-intercept with the slope `3/1`

We see that when y=5, the slope intersects at the point (-1,5).