Question

What is the equation, in point-slope form, of the line that

is perpendicular to the given line and passes through the
point (-4,-3)?

Answer 1

The equation of the line is
`y + 3 = m(x + 4)`, in which m is found as such
`am = -1`, considering a the slope of the given line.

Explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

`y - y_0 = m(x - x_0)`

In which m is the slope and the point is
`(x_0,y_0)`

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Passes through the point (-4,-3)

This means that
`x_0 = -4, y_0 = -3`

So

`y - y_0 = m(x - x_0)`

`y - (-3) = m(x - (-4))`

`y + 3 = m(x + 4)`

The equation of the line is
`y + 3 = m(x + 4)`, in which m is found as such
`am = -1`, considering a the slope of the given line.