Assuming the dot in #1.4# is actually a decimal point, and not multiplication.
The general rule says that you can add/subtract the same number to/from both sides, or multiply/divide both sides by the same number and the equation will be equivalent (represents the exact same relationship between #x# and #y#). Therefore:
#1.4x - 4y = 1 => 1.4x cancel(-4y) cancel(+4y) = 1 + 4y#
#=> 1.4x -1 = cancel(1) + 4y cancel(-1)#
#=> 1.4x -1 = 4y => 4y = 1.4x - 1#
First step, add #4y# to both sides, then subtract #1# from both sides, and finally you can switch sides on equalities (#a = b => b=a#).
Slope-intercept form of a line
It's the form #y = ax + b#, where #a# is the slope and #b# the #y#-axis intercept (and none other, you need to have a #y# without any coefficients). So, we need to take the equation we found, then divide everything by #4#:
#4y = 1.4x - 1 => y = ((1.4x - 1))/4 => y = (0.35x - 0.25)#. To graph this line, first write the equation in slope-intercept form. Then, simply pick any #x# value other than zero, substitute it in the equation, then solve for #y#, then plot that point on the graph. That point is on the line. Then, notice that based on the slope-intercept form, #b=-0.25=-1/4#, so plot the point on the #y# axis at #-1/4# (that's what is meant by #y# intercept).
Finally, connect both points and extend the line. The graph should look like this:
graph{y = 0.35x - 0.25 [-10, 10, -5, 5]}
---Side note---
If the #2.4# on the second case you provided in the question is meant to be #1.4#, then the second case is not correct, since you can subtract #1.4x# from both sides, but you get a #color(red)(-1.4x) + 1# instead of the #1.4x + 1#.
