geometry help!?

Question

Can you help me with this and explain how you got the answers? Thanks!

1. Write the equation of the line perpendicular to 9x + 2y = 18 and passes through the point (1, 4).

a. 9x - 2y = 1
b. 9x + 2y = 17
c. 2x - 9y = -34
d. 2x + 9y = 38


2. Write the equation of the line parallel to x = -16 and passes through the point (9, -10).

a. y = -6
b. y = -10
c. x = 9
d. x = -10


3. Determine if the lines 9x - 2y = 16 and 2x - 9y = -18 are parallel, perpendicular, or neither.

Answer 1

1.line perpendicular will have a slope which is the negative reciprocal of the slope of the givenline
slope of the given line =-9/2
so slope of the required line=2/9
passes through (1,4)
so the equation is y-4=2/9(x-1)
9y-36=2x-2=>2x-9y+34=0 or choice (c)
2.parallel lines will have the same slope
slope of the given line is 1/0
so the equation of the required line is
y+10=1/0(x-9) or x=9 choice (c)
3.slopes of the two lines are 9/2 and 2/9
so the answer is nither since the slopes are neither equal nor is the slope of one the negative reciprocal of the slope of the other

Answer 2

1, 9x + 2y = 18
--> 2y = 18-9x
--> y = 9 - 4.5x
slope of the equation = -4.5 or - 9/2

the line perpendicular to 9x + 2y = 18 has a slope of 2/9
i.e. y = 2/9 x + c

as it passes through the point (1, 4), we can find c
4 = 2/9 + c
c = 4 - 2/9 = 34/9

the equation is: y = 2/9 x + 34/9
or 9y = 2x + 34
or 2x - 9y = -34
answer: c

2. if you draw x = -16, you will find that the line has infinite slope or the line is vertical cutting the x-axis

the line parallel to x = -16 has infinite slope also and is vertical cutting the x-axis
therefore, equation: x = c

as it passes the point (9, -10), c = 9

answer: c. x = 9

3. 9x - 2y = 16
--> 2y = 9x - 16
--> y = 4.5x - 8

slope of the line: 9x - 2y = 16 is 4.5 or 9/2

2x - 9y = -18
--> 2x+18 = 9y
--> y = 2/9 x + 2

slope of the line: 2x - 9y = -18 is 2/9

if the slopes of the lines are equal, the lines are parallel
if the multiple of the 2 slopes equals -1, the lines are perpendicular

9/2 * 2/9 = 1 (not -1)
thus, the 2 lines are neither parallel nor perpendicular

Answer 3

for (2) x=-16 is a vertical line passing thru (-16,0). the only vertical line that goes thru (9,-10) is x=9

for (3) rewrite the equation as y=mx+c and if the m in both is equal, they are parallel. If the two m's myltiply and give -1 they are perpendicular. 9x-2y=16 can be written as y = 9/2 x - 8. 2x-9y = -18 can be written as y = 2/9 x + 2. If you multiply the two m's you get 1, so they are not perpendicular or parallel

Answer 4

I wont solve them completely for you... so that u understand the concepts, which is more important. The concepts involved are:

Let the equation of any line be:
ax + by = c

Then, the slope of this line is given by m1 = -a/b
(Slope is basically, the tanget of the angle that the line makes with the X axis)

Any line parallel to this will have the same slope
Any line perpendicular to this will have the slope (-m1) i.e. a/b

Also, an equation of a line is given by:
y = mx + c

m is the slope and c is the y intercept i.e.the point where the line crosses the Y axis.
Now, if you know a point where this line passes through, just plug in the values of x, y and m and find c. So, you can find the equation of the line y = mx + c.

Answer 5

1.)
9x + 2y = 18
2y = -9x + 18
y = (-9/2)x + 9

(1,4), m = (2/9)
4 = (2/9)(1) + b
4 = (2/9) + b
36 = 2 + 9b
34 = 9b
b = (34/9)

y = (2/9)x + (34/9)
9y = 2x + 34
-2x + 9y = 34
which is the same as saying
2x - 9y = -34

ANS : c.) 2x - 9y = -34

--------------------------------------------

2.)
x = 9

ANS : c.) x = 9

----------------------------

9x - 2y = 16
-2y = -9x + 16
y = (9/2)x - 8

2x - 9y = -18
-9y = -2x - 18
y = (2/9)x + 2

ANS : Neither

Answer 6

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