Well done in spotting a common problem in text books and teaching that hardly ever gets explained to students.
LINE EQUATIONS are in the form y=mx+c and make a straight line when graphed with gradient m and y intercept c.
LINEAR ALGEBRA is solving expressions like (x-3)/2=5 or 2x/5 = -2 or 3x+2 = 2x+9. notice there are only x's to the power of 1, with the one not even showing. Non-linear algebra is things like y=x^2, ie powers not equal to 1.
Algebra is soooo badly taught, mostly because of the high numbers of under-qualified maths teachers set loose on junior high school students. Its so illogical to start with piles of rules and letters, they should start with puzzles and patterns before useful equations like speed, area, finance, tax and regulations.