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

2 Answers
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"

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)