How do you write the equation in point slope form given (-3,-5) and (3,-15)?

2 Answers
Jim G.
Mar 23, 2018

#y+5=-5/3(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)=(-3,-5)" and "(x_2,y_2)=(3,-15)#

#rArrm=(-15-(-5))/(3-(-3))=(-10)/6=-5/3#

#"use either of the 2 given points for "(x_1,y_1)#

#"using "m=-5/3" and "(x_1,y_1)=(-3,-5)#

#y-(-5)=-5/3(x-(-3))#

#rArry+5=-5/3(x+3)larrcolor(red)"in point-slope form"#

jk.13
Mar 23, 2018

#(y+5)=-5/3(x+3)#

Explanation:

Point slope form is #(y-y_1)=m(x-x_1)#
First, find the slope by using #m=(y_1-y_2)/(x_1-x_2)#
#(-15+5)/(3+3)=-10/6=-5/3=m#
Then, choose one of the coordinate pairs (let's use #-3,-5#) and plug those in for #y_1# and #x_1# and also plug in the slope for #m#.
We get: #(y+5)=-5/3(x+3)#

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