Answer:
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
∵ [tex]\frac{-2y}{-2}=\frac{6}{-2}-\frac{4x}{-2}[/tex]
∴ 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
