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given two points find the equation

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3 Answers

  It should say points of a line.
 
 ( 0, 3 ) ( 2,6)
 
 
   L:  Y = mx +b       ?equation of a line in general.
 
       Line passes through 2 lines:
 
 
       m = 6 - 3  =  3      b = 3 / Y-Intercept is given
               2-0       2
 
         Y= 3/2x + 3
 
 Do the b yourself by following the same procedure., 
   
Hi Mondrea;
b. (0,3) (2,6)
Let's first establish slope.  This is the change-of-y divided by change-of-x...
(y-y1)/(x-x1)
(3-6)/(0-2)
-3/-2
A negative number divided by a negative number has a positive result.
3/2
Point-slope formula is...
y-y1=m(x-x1)
We need to use one point.  I randomly select the first...
y-3=(3/2)(x-0)
y-3=(3/2)x
Let's add 3 to both sides...
y=(3/2)x+3
The formula is now in the format of...
y=mx+b
m is the slope.
b is the y-intercept, the value of y when x=0.
Let's plug-in the other point to verify.
y=(3/2)x+3
6=(3/2)(2)+3
6=(6/2)+3
6=3+3
6=6
It works!
Mondrea,
 
Given two points, you need to develop two equations using each set of points and solve for the unknown slope and intercept i.e. y = mx + b
 
So for problem A, the first set of points gives you this equation
1 = m(0) + b
and the second gives you this equation
-1 = m(4) + b
 
Solving the first gives b = 1, and substituting this into the second equation gives you
-1 = m(4) + 1
-2 = 4m
-2/4 = m or m = -(1/2)
 
So the equation for the line is y = -(1/2)x + 1
 
You can repeat this process for the points in problem b.  I hope this helps.  John