Question

Write an equation parallel to the given line. Write an equation perpendicular to the given line.

Answer 1

Please, post just one question at a time.  I am arbitrarily focusing on #24 this time thru. 
                                                                                         2x-3
2x - 4y = 3  can easily be solved for y:  2x-3=4y, or y = ---------
                                                                                            4

The slope of this line is m = 2/4, or m = 1/2.

We need the equation of a new line parallel to this one.   Use the slope-intercept form of the equation of a straight line:  y = mx + b.

Let m = 1/2 and arbitrarily choose y-intercept b = 0.  Then we have

y = (1/2)x + 0, or y = (1/2)x.

Want the equation of a line perpendicular to 2x - 4y = 3?

We already know that the slope of this given line is 1/2.  The slope of a line perpendicular to this given line is the neg. reciprocal of 1/2, or m = -2.

Again, use the slope-intercept formula y = mx + b:

y = -2x + 0 (my choice of b = 0 is arbitrary; could have chosen some other value for b)