Question

what is the equation in point slope form of the lines through point P(2,0) that are a) parallel to, and b) perpendicular to the line x+2y=3

Answer 1

x+2y=3

let us find slope of this by comparing it to y=mx+b

y=-x/2 -3/2

slope (m) = -1/2=-0.5.............(1)

Now we find equation of line parallel to this passing through point P(2,0)

Two parallel lines have equal slopes so slope of this line would also be -0.5

using slope -0.5 and point P(2,0) we find y intercept

y=mx+b

0=-1/2(2) +b

b=1

using slope m =-0.5 and y intercept b=1 we get the equation of parallel as

y=-0.5x +1 (equation of parallel)

Next we find slope of perpendicular.

the product of slopes of perpendiculars is -1

so slope of perpendicular =2

using point (2,0) and slope =2 in slope intercept form to get y intercept ,

y=mx+b

0=2(2) +b

b=-4

plugging m=2 and b=-4 in slope intercept form to get equation of perpendicular

y=2x-4 equation of perpendicular