How do I write the equation of the line containing (2, 1) and (6, -1)?

Question

Can someone help me? I can't remember how to do this problem:

Write the equation of the line containing the points (2, 1) and (6, -1)

Answer 1

(x, y) = (2, 1)
(a, b) = (6, -1)

You are looking for the equation
y = mx + c
and need to find m and c.

For m, use the formula
m = (y - b) / (x - a) = (1 - (-1)) / (2 - 6) = 2/(-4) = -1/2

For c, plug x,y and m into the equation of the line and express c:
y = mx + c
1 = -1/2 · 2 + c
1 = -1 + c
c = 2

So the equation of the line containing (2, 1) and (6, -1) is:

y = (-1/2)·x + 2

Hope this helps.

Answer 2

you could start by finding the slope as (change in y) over (change in x). Take the y components to start with. y goes from 1 in the first point to 2 in the 2nd point. That's a change in the y component of -2.

Now do the same for the x component. The x component goes from 2 in the first to 6 in the second point. That a change of 4.

So the slope is -2/4 = -1/2.

So far we have
y = mx + c
y = -(1/2) x + c.

Sub in a point to find c. i.e. sub in (2,1) putting x = 2 and y = 1 into y = -(1/2)x + c gives
1 = -(1/2) times 2 + c
1 = - 1 + c
so c = 2.

Our equation is y = -(1/2) x + 2.

We now need to sub in the second point to check our work. To check the point (6, -1) satisfies y = -(1/2) x + 2 m just put x = 6 and we see that
y = -(1/2) times 6 + 2
y = -3 + 2 = -1. So (6, -1) is indeed on the line y = -(1.2) x + 2.

Ans: y = -(1/2) x + 2.

Answer 3

When you are given two points on a line, the process to find the equation of a line going through the two points is as follows:

First find the slope m = (y2 - y1) / (x2 - x1) where x1,y1 is one point and x2,y2 is the other. Thus m = (1 + 1)/(2 - 6) = -1/2

Thus y = (-1/2) x + b. To find b substitute either of the points into this equation and find b. 1 = (-1/2) 2 + b or b = 2.

Final equation is y = (-1/2) x + 2

hope this helps, Mike R

Answer 4

Given two points, the equation of line passing them both is:
y - y1 / y2 - y1 = x - x1 / x2 - x1

y - 1 / -1 - 1 = x - 2 / 6 - 2
y - 1 / -2 = x - 2 / 4
Cross multiplying gives:
-2x + 4 = 4y - 4
4y = -2x + 4 + 4
4y = -2x + 8
y = -x/2 + 2

Answer 5

its slope=1+1/2-6= -1/2
the equation of the line is
y-1=-1/2(x-2). answer.

Answer 6

first find the slope:
m = (-1 - 1) / (6 - 2) = -1/2

second, find the equation:
y - 1 = -1/2 (x - 2)
y - 1 = -1/2x + 1
y = -1/2x + 2

Answer 7

the slop is -1/2
y -1= -1/2 (x - 2)
which simplifies to:

y= -1/2x +2

Answer 8

i think michael r should get this answer right cuz number 1 hes right and he said everything i was going to say and more,

Answer 9

(y-y1)/(x-x1) = (y2-y1)/(x2-x1)
(y-1))/(x-2) = (-1-1)/(6-2) = -1/2
-x+2=2y-2
-x -2y = -4
x+2y = 4