What is the equation in point-slope form and slope intercept form for the line given slope= 8/3,(-2,-6)?

Question

Abigail Allen · Accepted Answer

General point slope form :
#y-y_1 = m(x-x_1)#
for a given slope #m# and a point on the line #(x_1,y_1)# From the given data:
#y+6 = 8/3(x+2)# General slope-intercept form:
#y=mx+b#
for a given slope #m# and a y-intercept #b# From the given data
#y = 8/3x+b#
but we still need to determine the value of #b#
If we insert the values of the point #(x,y) = (-2,-6)#
#-6 = 8/3(-2)+b#
#b= -6 +16/3 = -6 +5 1/3 = -2/3#
and the slope-intercept form is
#y= 8/3x -2/3#

Nathan Axel · Answer

undefined Point-slope form: $ y - y_1 = m(x - x_1) $ where $ m = \frac{8}{3} $, $ (x_1, y_1) = (-2, -6) $

Substituting the values:

Point-slope form: $ y - (-6) = \frac{8}{3}(x - (-2)) $
                $ y + 6 = \frac{8}{3}(x + 2) $

Slope-intercept form: $ y = mx + b $ where $ m = \frac{8}{3} $

Substituting the point $ (-2, -6) $ to find $ b $:

$ -6 = \frac{8}{3}(-2) + b $
$ -6 = -\frac{16}{3} + b $
$ b = -6 + \frac{16}{3} $
$ b = -6 + \frac{16}{3} $

$ b = -\frac{18}{3} + \frac{16}{3} $
$ b = -\frac{2}{3} $

So, the equation in slope-intercept form is $ y = \frac{8}{3}x - \frac{2}{3} $.