Question

Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation.
Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line. 

Answer 1

The point-slope form of the equation of the line is:

(y - y1) = m (x - x1)

So, (y + 2) = - 1/3 (x - 4) in the point-slope form is:

 [y - (-2) ] = (-1/3) [ x - 4 ]

You must, then realize that the line passes through the point (4,-2) and its slope is - 1 /3.

That slope, -1 / 3, means that the function is decresing (because the slope is negative),  and it decreases one unit when x increases 3 units.

Now you can fill in the blanks in this way:

Plot the point  (4, -2), move 1 unit down, and 3 units over to find the next point on the line.