Question

Write the equation of the line perpendicular to y = 2x + 1 and passing through the point (-2,3).

Answer 1

ok

the general form of a straight line is

y=mx + c

compare that to YOUR equation

y= 2x+1

what is the value equivalent to m, in YOUR equation?

Answer 2

the value that is equal to m is 2 . but i need perpendicular

Answer 3

OK - we're getting there

m is the slope of the line

the slope of a line perpendicular to that is -1/m

so if the slope is 2 - what is the slope of the perpendicular line?

Answer 4

-1/2

Answer 5

ok good

so the equation of the perpendicular line is of the form

y = -1/2 x +b

but you are told that when x=-2 then y =3 (because the point given lies on the line)

so put those values into the equation, and you can then work out what b is

Answer 6

3=2(-2)+1

Answer 7

no - it is
y= (-1/2) x +b

Answer 8

put y = 3, and x= -2

you will then have an equation with b as the unknown value

Answer 9

b=2

Answer 10

so you now know m and b

so write the new equation

y = mx+b

Answer 11

y=-1/2+2

Answer 12

yes - just about...
it's y = -1/2 x + 2

well done.

Just remember -
if you have a line of slope m then the perpendicular line has slope -1/m