Which equation is the slope-intercept form of the equation of the line that passes through (1, 2) and is parallel to 4x - 2y = 6?

The equation of the parallel line is y = 2x  

Step-by-step explanation:

The slope-intercept form of the linear equation is:

y = m x + b, where

Parallel lines have the same slopes and different y-intercepts

∵ The equation of the given line is 4x - 2y = 6

→ To find the slope of this line re-arrange it to be in the

   slope-intercept form Subtract 4x from both sides to move x to

   the right side

∵ 4x - 4x - 2y = 6 - 4x

∴ -2y = 6 - 4x

→ Divide both sides by -2 to make the coefficient of y = 1

∵

∴ y = -3 - (-2x)

∴ y = -3 + 2x

→ Swithch -3 and 2x

∴ y = 2x - 3

→ Compare it by the form of the equation above to find m

∴ m = 2

∴ The slope of the given line is 2

∵ The two lines are parallel

∴ The slope of the parallel line is 2

→ Substitute it in the form of the equation above

∴ y = 2x + b

→ To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The line passes through the point (1, 2)

∴ x = 1 and y = 2

∵ 2 = 2(1) + b

∴ 2 = 2 + b

→ Subtract 2 from both sides to find b

∴ 2 - 2 = 2 - 2 + b

∴ 0 = b

∴ y = 2x

The equation of the parallel line is y = 2x