Question

How do you find the slope of the line perpendicular to `4x+2y=10`?

Answer 1

• The Product of the Slopes of 2 Perpendicular Lines is always `-1`

• So let's find the Slope of the given line first

The equation of the line is `4x+2y=10`

The Slope Intercept form of the equation of a given line is `y=mx+c` where `m` is its slope, and `c` is its Y intercept.

To get the slope intercept form of the given line, we transpose `4x` to the other side. We get

`2y=-4x+10`

Dividing both sides of the equation by 2, we get:

`y = -2x + 5`

The Slope of the given line is `-2`. Let's call it `m_1`. And let the slope of the line Perpendicular to this line be called `m_2`

• As the Product of the Slopes of 2 Perpendicular Lines is `-1`, we can say that
  `m_1*m_2=-1`
  `(-2)*m_2=-1`
  `m_2=1/2`

• The Slope of the line Perpendicular to `4x+2y=10` is `1/2`