What is the equation in point-slope form and slope intercept form for the line given (-3,6) and (2,-9)?

1 Answer
May 4, 2015

The point-slope form is #y-6=3(x+3)#, and the slope-intercept form is #y=3x+15# .

Determine the slope, #m#.

#m=(y_2-y_1)/(x_2-x_1)# .

Let #(-3,6)=x_1,y_1# and #(2,-9)=x_2,y_2# .

#m=(-9-6)/(2-(-3))=15/5=3#

Point-slope Form

The general formula is #y-y_1=m(x-x_1)#

Use one of the points given as #x_1# and #y_1#. I'm going to use point #(-3,6)# which is consistent with finding the slope.

#x_1=-3#
#y_1=6#
#m=3#.

#y-6=3(x-(-3))# =

#y-6=3(x+3)#

Slope-intercept Form

The general formula is #y=mx+b#, where #m# is slope and #b# is the y-intercept.

Solve the point-slope form equation for #y#.

#y-6=3(x+3)#=

Add #6# to both sides.

#y=3(x+3)+6# =

Distribute the #3#.

#y=3x+9+6# =

#y=3x+15#

The slope is #3# and the #y#-intercept is #15#.