What is the point slope form of the equation (-6,6), (3,3)?

2 Answers
Mar 18, 2018

see below.

Explanation:

First, we need to find gradient of slope that cross between #(-6,6)# and #(3,3)# and denotes as #m#. Before this let #(x_1,y_1)=(-6,6)# and #(x_2,y_2)=(3,3)#

#m=(y_2-y_1)/(x_2-x1)#
#m=(3-6)/(3-(-6))#
#m=-1/3#

According to "http://www.purplemath.com/modules/strtlneq2.htm", the point slope form is #y-y_1=m(x-x_1)#

From above, using #(-6,6)# the point slope form is #y-6=-1/3(x-(-6))# and simplied it becomes #y=-1/3x+4#

How about second point? It produce same answer as equation that using the first points.

#y-3=-1/3(x-3)#
#y-3=-1/3x+1#
#y=-1/3x+4# (prove)

Mar 18, 2018

#y-3=-1/3(x-3)#

Explanation:

#"the equation of a line in "color(blue)"point-slope form"# is.

#•color(white)(x)y-y_1=m(x-x_1)#

#"where m is the slope and "(x_1,y_1)" a point on the line"#

#"to calculate m use the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(-6,6)" and "(x_2,y_2)=(3,3)#

#rArrm=(3-6)/(3-(-6))=(-3)/9=-1/3#

#"using "m=-1/3" and "(x_1,y_1)=(3,3)" then"#

#y-3=-1/3(x-3)larrcolor(red)"in point-slope form"#