Question

What is the solution for 4x-y=11?

Answer 1

See below:

Explanation:

There are an infinite number of solutions of `4x-y=11` - and they all lie along a line.

Graphically, it looks like this (at least in the range that we can see:)

graph{4x-11 [-32.47, 32.48, -16.24, 16.23]}

We can find specific points on this line, for instance the x-intercept (found by setting `y=0`)

`4x-0=11`

`x=11/4=>(11/4,0)`

And the y-intercept (by setting `x=0`):

`4(0)-y=11`

`y=-11=>(0,-11)`

We can talk about the slope of the line via a few different methods - I'll do it by shifting the line to slope-intercept form (the general form of which is `y=mx+b; m= "slope", b= "y-intercept"`):

`y=4x-11`

and so the slope if 4.