How do you write an equation in point slope and slope intercept form given point (3,2) and has a slope of -2?

Question

Abigail Allen · Accepted Answer

Point Slope Form: #y-2=-2(x-3)#
Slope Intercept Form: #y=-2x+8# The point-slope form formula is #y-y_1 = "slope" * (x-x_1)#. Here #x_1# #(3)# and #y_1# #(2)# are the coordinate points from your ordered pair #(3, 2)#. Plug in those values, along with the slope, and you have an equation in point-slope form. Looking at this equation, you are able to distribute the #-2# (slope) to the values inside the parenthesis, and you can also isolate the #y# by adding the #2# from the "y" side to the other side. You'll end up with #y=-2x+8# which is written in slope intercept form #y=mx+b# Here #m# stands for slope and #b# stands for the #y#-intercept.

Genesis Allen · Answer

undefined Point-slope form: $ y - y_1 = m(x - x_1) $ 
Given point: $ (3, 2) $ 
Given slope: $ m = -2 $

Substitute the given point and slope into the point-slope form: 
$ y - 2 = -2(x - 3) $

Now, simplify and solve for y to convert it to slope-intercept form: 
$ y - 2 = -2x + 6 $ 
$ y = -2x + 6 + 2 $ 
$ y = -2x + 8 $

So, the equation in slope-intercept form is $ y = -2x + 8 $.