Algebra help!! please. :]?

Question

1.) Find the slope of a line perpendicular to 4x+5y=7
a.)4/5
b.)5/4
c.)-4/5
d.)-5/4

For questions 2-4, identify wheather the lines for each pair of equations are parallel,perpendicular, or neither
2.)y=3x-1, y=-1/3x+2
a.)parallel
b.)perpendicular
c.)neither

3.)y=2x+5, 2x+y=-4
a.)parallel
b.)perpendicular
c.)neither

4.)y=-2/3x-1, 2x+3y=6
a.)parallel
b.)perpendicular
c.)neither

5.)Select the equation of the line that contains (2,1) and it is perpendicular to y=-1/2x+3
a.)y=-1/2x-3
b.)y=1/2x-3
c.)y=2x-3
d.)y=-2x-3

THANKS SOOO MUCH!

Answer 1

Two lines are parallel if their slope is the same and they have a different y intercept. (If the slope is the same and they have the same y intercept, the two lines are the same line.)

Two lines are perpendicular if their slopes are inverse to each other with the opposite sign -- for example, lines with slopes of 1/3 and -3 are perpendicular. (That's called a negative reciprocal.)

Any other relationship between the two lines means they'll intersect, but not at right angles.

You can easily see these relationships by putting the equations in the slope-intercept form y = mx + b and looking at the slopes and intercepts.

So in the first problem, get the y alone on the left side of the equation. 5y = -4x + 7 and y = (-4/5)y + 7/5. The slope is -4/5, so the slope of a line with a negative reciprocal is 5/4.

In 2 through 4, put all the equations in slope-intercept form, with "y =" alone on the left side. Not "2y =" or "4y/5 =" or anything else: You have to have a single y alone on the left side.

Now just look at the slopes, which are the factors of x. If they're identical, the lines are parallel. If the slopes have different signs and one is the reciprocal of the other, they are perpendicular. In all other cases, they're neither.

In the last problem, you want a slope that is the negative reciprocal of (-1/2). Turn the fraction upside down and reverse the sign and you've got the equation of the line.

You've already solved the problem, because there's only one answer with the correct slope. If there was a choice e), "none of the above," you'd have to keep going to find the line that contains (2,1). You do that by taking the slope-intercept general equation and plugging in numbers. y = mx + b, and you know x (2), y (1) and m (2). You want to solve for b, and sure enough, b = -3.

In problems like these, don't worry about the b in y = mx + b if the question is only "parallel, perpendicular or neither." If the slopes are negative reciprocals, the lines are perpendicular somewhere. The b term only tells you where on the first line the second line will cross it.

Answer 2

1. -5/4
2. Perpendicular
3. Neither
4. Parallel
5. y=2x-3

Answer 3

-1/(-4/5) = 5/4

Perpendicular besause product of slopes = -1

neither because slopes not equal or negative reciprocals

parallel because slopes same and y-intercept different

y= 2x-3

Answer 4

Now how are you going to learn algebra if you have Y.A. doing your homework for you? Wow, I sound like your mom.

Answer 5

1)a
2)b
3)c
4)a
5)c