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

Question

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

Answer 1

first manipulate the terms from standard form to slope
2y = -9x + 18
y = -9x/2 + 9

for the line to be perpendicular, the slope must be the negative reciprocal. Therefore, the slope is 2x/9

y = 2x/9 +b
4 = 2/9 +b
b = 34/9

thus the equation is y = 2x/9 +34/9
in standard form, this is
2x - 9y = -34


next:

x = 9
this is because any equation with x =
means that it is vertical. therefore all you have to do is find the equation of x = with the x value that you want

x = 9

Answer 2

2 strains are perpendicular if their gradients multiply jointly to get a million. So even though the gradient of a million of the strains is, the different gradient could desire to be the reciprocal. placed 9x + 2y = 18 in gradient intercept variety. 2y=18-9x y=9-9/2x y=-9/2x+9 for all of the equations, placed them in gradient intercept variety. (y=mx+b) a) 9x-2y=a million -2y=a million-9x y=-a million/2+9/2x y=9/2x-a million/2 b) 9x + 2y = 17 2y=17-9x y=17/2-9/2x y=-9/2x+17/2 c) 2x - 9y = -34 -9y=-34-2x y=-34/-9+2/9x y=2/9x+34/9 d) 2x + 9y = 38 9y=38-2x y=38/9-2x/9 y=-2x/9+38/9 the different perpendicular line could desire to be c or d as a results of fact they're the only 2 strains whose gradient is the reciprocal of 9/2. For the ingredient (a million,4)=(x,y) x=a million y=4 For c. y=2/9x+34/9 and d. y=-2/9x+38/9, placed the x and y values into the equations. c. 4=2/9(a million)+34/9 4=2/9+34/9 4=36/9 4=4 This line DOES bypass via the ingredient (a million/4) d. 4=-2/9(a million)+38/9 4=-2/9+38/9 4=36/9 4=4 This line DOES bypass via the ingredient (a million/4) the two those factors stay via the line (a million,4) and characteristic a reciprocal of 9/2. hence they're the two perpendicular to the line 9x + 2y = 18 answer: C and D

Answer 3

Question 1
2y = - 9x + 18
y = (- 9/2).x + 9-------m = - 9/2
Gradient of perpendicular = 2/9
y - 4 = (2/9).(x - 1)
y = (2/9).x - 2/9 + 36/9
y = (2/9).x + 34/9
or
9y = 2x + 34
2x - 9y + 34 = 0

Question 2
x = 9 is required equation.
(this is a vertical line)

Answer 4

First find the slope of the line
2y = -9x + 18
y = - 4.5x + 9

The perpendicular slope therefore is 1/4.5 (ie. the negative reciprocal)
since the line passes through (1,4)


1/4.5 = (y-4)/(x-1)
x-1 = 4.5(y-4)
x-1 = 4.5y - 18
4.5y = -x -17
9y = -2x -34

To find the parallel slope we know it is the same, ie. m=0
Therefore the equation of the line is x=9

Answer 5

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

perpendicular is the slope with the negative recipricol: 2/9
therefore, y-4=2/9(x-1)

x=-16

parallel is same slope: 0

x=9

Answer 6

2y=-9x+18
y=-9/2 x+9
m=-9/2
y-y1=m(x-x1)
y-4=-9/2(x-1)
y=-9/2 x +9/2 +4
y=9/2 x+ 17/2