Write an equation of the line passing through point P(4,0) that is parallel to the line -x + 2y = 12.

Answers

Answer 1
arallel lines have the same slope
-x+2y=12
2y=x+12
y=(1/2)x+6
the slope is 1/2
using the point-slope form of a line...
y-y1=m(x-x1) where m is the slope and (x1,y1) is (4,0)
y-0=(1/2)(x-4)
y=(1/2)x-2 is the equation of the line
check: 0=(1/2)(4)-2
0=2-2
0=0
Answer 2
Answer: y= 1/2x-2
___________________
Explanation:

-x+2y=12
2y=12+x
divide both sides by 2
y= 6+ x/2
as they are parallel, therefore, their slopes are equal
hence,
put P(4;0) in the equation to find y intercept( y=kx+b, there b is y intercept)
0= 1/2 * 4+ b
b=-2
hence,
our equation is
y=1/2x-2
Hope it helps :)


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Step-by-step explanation:

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Step-by-step explanation:

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Write the equation of the line that in slope-intercept form with the given point and slope or two points. (-4. 6); slope = -3/4

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Answer:

y = -3/4x + 3

Step-by-step explanation:

6 = -3/4(-4) + b

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What is the y-intercept of the function y = 3x + 33 ?

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Step-by-step explanation:

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Step-by-step explanation:

The resultant of the vectors a = 3i - 2j and b = pi - 2pj is parallel to the vector c = 2i - 3j.
a) Find the value of p
b) Find the resultant of vectors a and b.

Please help me with this question, thank you ​

Answers

Part (a)

The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.

You can use the parallelogram law as a visual alternative.

Adding a and b leads to

a+b = (3i-2j) + (pi-2pj)

a+b = (3i+pi) + (-2j-2pj)

a+b = (3+p)i - (2+2p)j

Define vector d to be d = a+b so we can use it later below.

Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.

We can say the following

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

(3+p)/(2) = (-(2+2p))/(-3)

Let's solve for p

(3+p)/(2) = (-(2+2p))/(-3)

(3+p)/(2) = (2+2p)/3

3(3+p) = 2(2+2p) .... cross multiply

9+3p = 4+4p

4p+4 = 3p+9

4p-3p = 9-4

p = 5

Answer:  p = 5

========================================================

Part (b)

Since p = 5, from part (a), we can determine vector b

b = pi - 2pj

b = 5i - 2*5j

b = 5i - 10j

Then add vectors a and b to get

a+b = (3i-2j) + (5i - 10j)

a+b = (3i+5i) + (-2j - 10j)

a+b = (3+5)i - (2+10)j

a+b = 8i - 12j

Or we can say

a+b = (3+p)i - (2+2p)j  .... from part (a)

a+b = (3+5)i - (2+2*5)j ... plugging in p = 5

a+b = 8i - 12j

Note the ratio of the components of vector d and vector c are such

(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)

8/2 = -12/(-3)

4 = 4

This helps confirm the answer

You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines

Answer:  8i - 12j

a.

The value of p is 5

Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b

= 3i - 2j + pi - 2pj

= (3 + p)i - 2(1 + p)j

Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.

The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.

So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]

= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)

= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0

= -3(3 + p)k + 4(1 + p)k

= [-3(3 + p) + 4(1 + p)]k

= [-9 - 3p + 4 + 4p)]k

= [-9 + 4 - 3p + 4p)]k

=  [-5 + p]k

[-5 + p]k = RcsinФ.

Since R and c are parallel, Ф = 0°

So, Rcsin0° = Rc × 0 = 0

So,   [-5 + p]k = 0

-5 + p = 0

p = 5

The value of p is 5

b.

The resultant of vectors a and b is R = 8i - 12j

Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j

Substituting the value of p = 5 into r, we have

R = (3 + p)i - 2(1 + p)j

R = (3 + 5)i - 2(1 + 5)j

R = 8i - 2(6)j

R = 8i - 12j

So, the resultant of vectors a and b is R = 8i - 12j

Learn more about resultant of vectors here:

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Answer:

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Answers

Explanation:

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