parallel and perpendicular lines, please help ! a level maths?

Question

line 1 has equation y=2x+5, and line 2 has equation 3x+py=14, where p is a constant, how do i find the value of p in the cases:
a) line 1 is parallel to line 2
b) line 1 is perpendicular to line 2?

Answer 1

a) Re-arrange the second equation so it is in the form y = ax + b
So 3x+py = 14
py = 14 - 3x
y = 14/p - 3x/p
Where the lines are parallel, they have the same equation of the slope, i,e. gradient, so the x's must be the same in each equation. So -3x/p = 2x
so -3/p = 2
2p = -3
so p = -3/2

(ii) When the lines are perpendicular, the gradient of one line is -1/gradient of the other line.
So: 3x/p = x/2
3/p = 1/2
p/2 = 3
p = 6

There you go, hope that makes sense! :D

Answer 2

a) parallel lines have the same gradient. Therefore in (1) the coefficient of 'x' is 2, - this is the gradient of the line.
Hence for (2) 3x + py = 14
py = -3x + 14
y = -3/p(x) + 14/p
So for lines 1 & 2 to be parallel then 2 = -3/p
p = -3/2
Careful with this one :: -3 divided by -3/2 = 2
b) for lines to be perpendicular they must satisfy the equation
mm' = -1 (where m & m' are the gradients)
So using (1) Gradient 2 then
2 x m' = -1
m' = -1/2 (gradient of (2) perpendicular to (1)).

Answer 3

Line 1: y = 2x + 5 m = 2
Line 2: py = -3x + 14 so y = -3/p x + 14/p
a) For parallel lines 2 = -3/p so p = -3/2
b) For perpendicular lines 2 x -3/p = -1
-3/p = -1/2
p = 6

Answer 4

a) If they are parallel, they have the same slope. Line 1 has slope 2 (y=mx+b, m=slope)

Slope can also be expressed by -b/a, where a=x-intercept, b=y-intercept. The x-intercept in line 2 is 14/3 (when y=0), while the y=intercept is 14/p (when x=0).

-(14/p)/(14/3)=-3/p, so the slope of line 2 is -3/p, which equals 2. For that to be true, p equals -3/2.

b) The only change here is that the slope of line 2 would be -1/2 (the additive reciprocal of the multiplicative reciprocal), so p equals 6.

Answer 5

Re-arrange your 2nd equation as: py = -3x + 14
Then as: y = (-3/p)x + 14/p

When lines are parallel, they have the same gradient M in the general equation y = Mx + c.
So for parallel lines, (-3/p) = 2 or p = -3/2

Perpendicular lines are formed when the M values multiply go give -1. So (-3/p) * 2 = -1 or -6/p = -1, or p = 6

Answer 6

First, rearrange the equations into the y=mx+c format where m represents the gradient (or slope) and c represents the y-intercept.

Line1: y = 2x+5
Line2: py = -3x+14 => y = (-3/p)x + (14/p)

a) Line1 is parallel to Line2 => the gradients are the same.
2 = (-3/p)
2p = -3
p = -3/2
p = -1.5

b) Line1 is perpendicular to Line2 => the product of their gradients result in -1. [m1 x m2 = -1]
2 x (-3/p) = -1
-6/p = -1
-6 = -p
p = 6

Answer 7

change 3x+py=14 to slope intercept form

y = (-3/p) x +(14/p)

slope is (-3/p)

slope of y=2x+5 is 2

a) for parallel lines, slopes are equal

therefore (-3/p) = 2

so that p = (-3/2)


b) for perpendicular lines, product of the slopes is (-1)

therefore (-3/p)*2 = (-1)

so that p = 6

Answer 8

the secon line can be written as y=-3/p*x+14/p
1) -3/p=2====> p= -3/2
2)-3/p=-1/2 3/p=1/2 p=6

Answer 9

first you come across the equation of the traditional line. from which you realize the gradient (m1) and your attempting to discover the gradient of the perpendicular line(m2) m1 x m2 = -a million m2 = -a million/m1 in case you realize the unique equation purely swap the gradients additionally the equation of a today line is y - y1 = m(x -x1) (x1,y1) being component on the line m being gradient

Answer 10

put in slope-intercept form y=mx+b
y= -3/px+14/p

parallel slopes are same
-3/p = 2

perpendicular is opposite reciprocal
-3/p= -1/2