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.