Question 367418
x - 4y = -24
m=
b=
<pre>
Your "target" is the slope-intercept form which you should
memorize:

{{{y = mx + b}}}

You first solve the equation for y

{{{x - 4y= -24}}}
   
Subtract x from both sides:

{{{-4y= -24+x}}}

To get rid of the {{{-4}}} multiply every term by {{{-1/4}}}

{{{expr(-1/4)(-4y)=expr(-1/4)(-24)+expr(1/4)x}}}

Simplify:

{{{y = 6 + expr(1/4)x}}}

Swap the terms on the right because you want it to look like y = mx+b

{{{y = expr(1/4)x+6}}}

Compare that to {{{y=mx+b}}}

And you see that 

{{{m =1/4}}} and {{{b=6}}}

"m" is the slope because it determines which way and how much the
line slants.  "b" is the number on the y-axis where the line
crosses the y-axis.

Now I'm going to go further than that, because you're going to have to.

That means the graph of the equation

{{{y = expr(1/4)x+6}}}

crosses the y-axis at (0,b) which is (0,6), called
the y-intercept.  We plot that point

{{{drawing(400,400,-5,5,-2,8, graph(400,400,-5,5,-2,8),

circle(0,6,.1)  )}}}

We take the numerator of the slope {{{1/4}}} which is 1.  The slope
is positive so we draw a line 1 unit up from the y-intercept, like this
in green:

 {{{drawing(400,400,-5,5,-2,8, graph(400,400,-5,5,-2,8),
green(line(0,6,0,7)),
circle(0,6,.1)  )}}}

Now we take the denominator of the slope {{{1/4}}} which is 4.  We draw 
a line 4 units right from where that green line ended up, like this, also
in green:

 {{{drawing(400,400,-5,5,-2,8, graph(400,400,-5,5,-2,8),
green(line(0,6,0,7),line(0,7,4,7)),
circle(0,6,.1)  )}}}

Next we take a ruler and draw a line through both the y-intercept and the
end of that second green line, like this:

 {{{drawing(400,400,-5,5,-2,8, graph(400,400,-5,5,-2,8),
green(line(0,6,0,7),line(0,7,4,7)), red(line(-8,4,8,8)),
circle(0,6,.1)  )}}}

That'e the graph of {{{y = expr(1/4)x+6}}}

Edwin</pre>