# Write an equation for the line that is parallel to the given line and passes through the given point. y=2x+4; (3,8)

A. y = 2x + 2
B. y = 2x + 6
C. y = -2x + 6
D. y = -1/2x + 2**

Am I correct?

## Slope(m) = 2, P1(3,8), P2(x,y).

m = (y-8)/(x-3)
2 = (y-8)/(x-3)
Cross multiply:
2(x-3) = (y-8)
2x-6 = y-8
Eq: Y = 2x + 2.

Check: Y = 2*3 + 2 = 8.

## I'm sorry, but the answer is not C or D, because a parallel line would have the same slope, which is 2. You are probably thinking of a perpendicular line, which would have a slope of -1/2. Try A or B.Hopefully you get it!

To find the equation of a line parallel to the given line, we need to use the same slope.

The slope of the given line is 2, so the equation of the line parallel to it will also have a slope of 2.

Now, let's use the point (3,8) to find the y-intercept (the value of y when x is 0).

Using the point-slope formula, we have:

y - 8 = 2(x - 3)

Now we can simplify:

y - 8 = 2x - 6

Rearranging the equation:

y = 2x - 6 + 8

y = 2x + 2

So, the equation of the line that is parallel to the given line and passes through the given point (3,8) is y = 2x + 2.

Therefore, the correct answer is A. y = 2x + 2. Great job!

## To find the equation of a line that is parallel to the given line and passes through the given point, you need to use the fact that parallel lines have the same slope.

The given line has a slope of 2 (since it is in the form y = mx + b, where m is the slope). Therefore, the parallel line will also have a slope of 2.

Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point (3,8), and m is the slope (2), we can substitute the values and find the equation:

y - 8 = 2(x - 3)

Expanding the equation:

y - 8 = 2x - 6

Rearranging the equation:

y = 2x - 6 + 8
y = 2x + 2

Therefore, the correct equation for the line that is parallel to y = 2x + 4 and passes through the point (3,8) is:

A. y = 2x + 2

## To find the equation of a line parallel to a given line and passing through a given point, follow these steps:

Step 1: Understand the relationship between parallel lines.
Parallel lines have the same slope. Therefore, the equation of the new line will have the same slope as the given line.

Step 2: Find the slope of the given line.
The given line equation is in the form y = mx + b, where m represents the slope. In this case, the given line is y = 2x + 4, so the slope is m = 2.

Step 3: Use the point-slope formula to find the equation.
The point-slope formula is y - y1 = m(x - x1), where (x1, y1) represents the given point and m is the slope. Substitute the values into the formula:
y - 8 = 2(x - 3)

Step 4: Simplify the equation.
Distribute the 2 on the right side:
y - 8 = 2x - 6

Step 5: Rearrange the equation.
Move the -8 to the other side by adding 8 to both sides:
y = 2x - 6 + 8

Simplify the equation further:
y = 2x + 2

Therefore, the correct answer is A. y = 2x + 2.