What is the equation of the line that is parallel to the line defined by the equation 8x = 2y + 4 and goes through the point (3, 2)?

Question

What is the equation of the line that is parallel to the line defined by the equation 8x = 2y + 4 and goes through the point (3, 2)?

Answer 1

First, start by finding the slope of the line, because parallel lines always have the same slope.

Rearranging into y=mx+b form, 8x=2y+4 can be rewritten as y=4x+2, which tells us that the slope of the line is 4.

Now, we can use this information to fill in the y=mx+b form of the line going through the point (3,2).

y=mx+b => 2 = m(3) + b and then fill in the slope which was previously stated to be 4.

Thus, 2 = 4(3) +b and then you can solve for b to get that b = -10.

From here, use the m and b values of 4 and -10 to write the equation of the line: y = 4x - 10

Answer 2

8x = 2y + 4

2y = 8x -4

y = 4x - 2 4 = the slope of the parallel line

y= 4x + b plug in the point to solve for b

2 = 4(3) + b

b =2 -12 =-10

y= 4x -10 is the parallel line through the given point

Answer 3

8x = 2y + 4

2y = 8x -4

y = 4x - 2 4 = the slope of the parallel line

y= 4x + b plug in the point to solve for b

2 = 4(3) + b

b =2 -12 =-10

y= 4x -10 is the parallel line through the given point