find the equation of the line that passes through (2,6) and is perpendicular to the line 2x+y+7=0

Question

i did it but my answer ends with 6=-6 making it wrong ....or am i right

Answer 1

First the equation 2x + y + 7 =0 needs to be in slope/intercept form which is y = mx + b.

 

To solve for y the equation is y = -2x - 7.

 

The you need to find the slope for the perpendicular line which is the negative reciprocal of the slope of the line, so the equation for the perpendicular line is y = x/2 + C.  Now you can solve for C by substituting for x and y for point (2,6)
6 = 2/2 + C

6 = 1 + C

6-1 = C

C = 5.

The equation is y = x/2 + 5.