What is the equation of a line parallel to 2x - 5y = 10 and passes through the point (5, -3)? *

Answer 1

standard form of linear equation is y = mx + b where m is gradient, b is y intercept.

rearrange 2x - 5y = 10 to get 5y = 2x - 10 then y = (2/5)x - 2

m = 2/5, b = -2 so gradient is 2/5 (up and to right, shallow, up 2 units across 5 units)

parallel lines must have the same gradient

hence, the general equation of parallel lines in this case is y = (2/5)x + n

we want the specific line y = (2/5)x + b passing through point (5,-3)

substitute point values to find b

(-3) = (2/5)(5) + b

-3 = 2 + b

hence b = -5

and the required equation of the line is y = (2/5)x - 5 OR 5y = 2x - 25

and finally double-check your work to make sure derived equation is parallel and passes through required point!

Answer 2

all parallel lines have the same slope

2x-5y = 10

5y = 2x-10

y = (2/5)x - 2

slope = 2/5

use the point slope formula

y-h = m(x-k) where m= 2/5 and (k,h) = (5,-3)

y+3 = (2/5)(x-5)

5y +15 = 2x-10

2x -5y = 25