Question

what is the equation of the line first written in point slope form and then written in slope intercept form? please show how you did it

Answer 1

We have the points (3, 21) and (6, 12).

The slope-intercept form: y = mx + b.

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{12-21}{6-3}=\dfrac{-9}{3}=-3\\\\y-21=-3(x-3)\qquad|\text{use distributive property}\\\\y-21=(-3)(x)+(-3)(-3)\\\\y-21=-3x+9\qquad|\text{add 21 to both sides}\\\\y=-3x+30$

Answer:

point-slope form: y - 21 = -3(x - 3)

slope-intercept form: y = -3x + 30