given two points find the equation

Question

A. (0,1)(4,-1)

 

 

 

b. (0,3) (2,6)

Answer 1

  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., 

   

Answer 2

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!

Answer 3

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