What is the equation of a line passing through (5,2) and parallel to the line represented by the equation y - 2x + 1?

Step-by-step explanation:

Im not sure if its supposed y = -2x + 1 or y = 2x + 1 but I'll solve the problem for both.

First for y = -2x + 1

Since the line has to be parallel to y = -2x + 1

the slopes would be the same.

so, so far the equation would be

y = -2x + b

now we substitute (5,2) into the equation

2 = -2(5) + b

2 = -10 + b (Add 10 to both sides of the equation)

+10 +10

12 = b

Now that we solved for b

The equation would be

y = -2x + 12

^^ This equation is parallel to y = -2x + 1

Now to solve for an equation parallel to y = 2x + 1

Both equations would have the same slope

So far we would have

y = 2x + b

Now we solve for be by substituting the point (5,2)

2 = 2(5) + b

2 = 10 + b (subtract 10 from both sides)

-10 -10

-8 = b

After solving for b

The equation is

y = 2x - 8

This equation is parallel to y = 2x + 1

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

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