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

$y-2=-\dfrac{1}{4}(x+3)\to m=-\dfrac{1}{4}$

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

$m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

Therefore the slope of ouer line is

$m=-\dfrac{1}{-\frac{1}{4}}=4$

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

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