Question

Write the equation of a line that is perpendicular to the given line and passes through the given point

y-2=-1/4(x+3);(-3,5)

Answer 1

The point-slope form:

`y-y_1=m(x-x_1)`

m - slope

We have the line

`y-2=-(1)/(4)(x+3)\to m=-(1)/(4)`

If m₁ and m₂ are the slopes of the perpendicular lines, then

`m_1m_2=-1\to m_2=-(1)/(m_1)`

Therefore the slope of ouer line is

`m=-(1)/(-(1)/(4))=4`

We have the point (-3, 5). Put the coordinates to the equation of a line in the point-slope form:

`y-5=4(x-(-3))\\\\\boxed{y-5=4(x+3)}`