What is an equation of the line that passes through the point (2,-5)(2,−5) and is parallel to the line x-2y=16x−2y=16?

Answer 1

Line x - 2y = 16

slope of equation of the general form ax + by = c is -a/b

here a = 1 and b = -2, so slope = 1/2

the slope of the line parallel to that line will also be 1/2

Line passes through (2,-5)

can create equation of line in point-slope form: y - y1 = m (x - x1) where m is slope and (x1,y1) are coordinates of point line passes through.

here we are given (x1,y1) = (2,-5) and since m = 2 we get:

y + 5= 1/2(x -2)

to put into general form, first multiply both sides by 2 to clear fractions:

2y + 10 = x - 2

move x to left side of equation by subtracting x from both sides:

-x + 2y + 10 = - 2

subtract 10 from both sides of the equation:

-x + 2y = -12