Writing the Equation of a Line Parallel to a Given Line

Question

Find the equation of the line parallel to the line y = 4x – 2 that passes through the point (–1, 5).

 

The slope of y = 4x – 2 is –4–224.

The slope of a line parallel to y = 4x – 2 is –4–224.

The equation of the line parallel to y = 4x – 2 that passes through the point (–1, 5) is y = –4x + 5–2x + 32x + 54x + 9.

Answer 1

Previous Line is y=4x-2

Equation of a Parallel line to Previous line (y=4x-2) is

y=4x+c

since new line is parallel to previous line., so slope of the new line (m) = same as previous line,

meaning m=4 for new line.

c is unknown intercept

New line passes through the point (-1, 5) so it must satisfy the new equation of the parallel line.

That means 5=4(-1) +c

Which means c=9

So equation of new Parallel line is y=4x+9

Answer y=4x+9