Question

Find the equation of a line that is parallel to 5x-2y=-12 and passes through (2,-3)

Answer 1

5x - 2y = 16

Explanation:

`k:\ A_1x+B_1=C_1\\\\l:\ A_2x+B_2y=C_2\\\\k\ \parallel\ l\iff A_1=A_2\ \wedge\ B_1=B_2\\==========================`

`\text{We have the equation of a line:}\\\\5x-2y=-12\\\\\text{Therefore the equation of a parallel line is:}\\\\5x-2y=C\\\\\text{Put the coordinates of the given point to the equation and solve for}\ C:\\\\(2,\ -3)\to x=2,\ y=-3\\\\C=5(2)-2(-3)\\C=10+6\\C=16\\\\\text{Finally:}\\\\5x-2y=16`