Question

Find the equation of the line that passes through (1,2) and is perpendicular to

y
=
2
x
+
3
.
Leave your answer in the form
a
x
+
b
y
=
c
Where
a
,
b
and
c
are integers.

Answer 1

x + 2y = 5

Explanation:

y = mx + b the m is the slope or gradient.

y=2x+3 The slope is 2.

When lines are perpendicular, the slopes are opposite inverses of each other. So, the perpendicular slope to 2 is -1/2. I would write the answer in the point slope of the line and then change the equation to the stand form

y -2 = -1/2(x -1) Distribute the -1/2

y - 2 = -1/2x + 1/2 Add 1/2 x to both sides

1/2x + y -2 = 1/2 Add 2 to both sides

1/2x +y = 5/2 Multiply by 2 to clear the decimal

x + 2y = 5