Question

Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6.

Answer 1

y + 9 = 6(x - 4)

the equation of a line in point-slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 6 and (a, b) = (4, - 9)

y + 9 = 6(x - 4) ← in point-slope form

Answer 2

Knowing the slope $m$ and a point $(x_0,y_0)$ of a line, the equation of the line is given by

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

Substitute your values to get

$y+9 = 6(x-4)$

You can rearrange this equation to write it in the slope-incercept form:

$y = 6x - 33$