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)
