The equation of a line a is given by 3y=x+12- Find line b that is parallel to line a and passes through the point (6, -8)

Answer:   3/4

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Explanation

The point (p,r) is on the line y = x+b

Plug in x = p and y = r to get r = p+b. Let's solve for b

r = p+b

b = r-p

This will be used later.

The point (2p,5r) is on the line y = 2x+b

Plug in those coordinates:

y = 2x+b

5r = 2*(2p)+b

5r = 4p+b

Next we replace b with r-p. This is valid because b = r-p.

5r = 4p+b

5r = 4p+r-p

5r = 3p+r

5r-r = 3p

4r = 3p

Then we follow the cross multiplication process in reverse.

4r = 3p

4r/4 = 3p/r

r = 3p/4

r/p = (3p/4)*(1/p)

r/p = 3/4  is the final answer

Final answer:

Using the given coordinates and equations, we find that the value of r/p is 3/4 after a process of subtracting and simplifying two equations.

Explanation:

The question is related to the linear equations in the xy-plane. Given two points, (p,r) and (2p,5r) which lie respectively on the equations y = x + b and y = 2x + b.

We have two points on two different lines:

• Point A: (p, r) lies on the line y = x + b.
• Point B: (2p, 5r) lies on the line y = 2x + b.

Substituting the coordinates of the first point into the first equation gives r = p + b. Similarly, substituting the coordinates of the second point into the second equation gives 5r = 2(2p) + b, which simplifies to 5r = 4p + b.

Now, subtract the first equation from the second to eliminate b, resulting in 5r - r = 4p - p, which simplifies to 4r = 3p.

Dividing by 4p gives us r/p = 3/4. So, the value of r/p is 3/4.

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Answer:78

Step-by-step explanation: