Question

Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept for.
(-6,6) and (9,1)
What is the​ point-slope form of the equation of the​ line?
What is the​ slope-intercept form of the equation of the​ line?

Answer 1

As we go from (-6,6) to (9,1), x increases by 15 and y decreases by 5.  Thus, the slope of this line is m = rise / run = -5/15, or m = -1/3.

Point-slope form:  y-6 = (-1/3)(x+6), using data from (-6,6).  

Slope-intercept form:  starting with y = mx + b, substit. -6 for x, 6 for y and -1/3 for m:

6 = (-1/3)(-6) + b, or

6 = 2 + b.  Then b = 4, and the equation in slope-intercept form is

y = (-1/3)x + 4.