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

1 Answer

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.