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

Question

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

Nathan Axel · Accepted Answer

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#.

Jameson Allen · Answer

undefined Point-slope form: y - y₁ = m(x - x₁) where m is the slope and (x₁, y₁) is a point on the line.

Slope intercept form: y = mx + b where m is the slope and b is the y-intercept.

Given points: (-3, 6) and (2, -9)

Calculate the slope: m = (y₂ - y₁) / (x₂ - x₁)
m = (-9 - 6) / (2 - (-3)) = (-15) / 5 = -3

Using point-slope form:
y - 6 = -3(x - (-3))
y - 6 = -3(x + 3)

Using slope intercept form:
y = -3x - 9