Home > Algebra > Write an Equation Given Two Points

Which equation represents the line that passes through the points (1, 1) and (-2, 7)?

Answer 1

Genesis Allen

#vec u =(-3; 6)#
#vec n=(6; 3)# or #vec n=(-6; -3)#

general equation:
#6x+3y+c=0#

final equation:
#2x+y-3=0#

#A[1; 1]# #B[-2; 7]#

Now you need to find the directional vector: #vec u = B - A# #vec u = (-3; 6)#

With this vector you are able to create the parametric equation, but I gues you want the general equation, so you will need the normal vector. You create the normal vector form directional by replacing x and y and changing one of signs. There are two solutions: 1. #vec n=(6;3)# 2. #vec n=(-6;-3)#

It does not matter which one of them you will choose.

General equation: #ax + by + c = 0# #6x+3y+c=0#

for A (#x=1; y=1#): #6*1 + 3*1 + c = 0# #c=-9#

Final equation: #6x+3y-9=0# #2x+y-3=0#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

The equation representing the line passing through the points (1, 1) and (-2, 7) is:

y = -2x + 3

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.