can the points (2,5) and (4,9) form an equation

Question

I am not coming up with an equal equation using the points (2,5) and (4,9), please help.  I have the slope as 4/2 or 2

Answer 1

Hi L;

(2,5) and (4,9)

Slope is change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

m=(5-9)/(2-4)

m=-4/-2

A negative number divided by a negative number has a positive result...

m=2

Point-slope formula...

y-y₁=m(x-x₁)

y-y₁=2(x-x₁)

Let's plug-in either coordinate.  I randomly select the second...

(4,9)

y-9=2(x-4)

y-9=2x-8

y=2x+1

Let's plug-in the other coordinate to verify...

(2,5)

5=[(2)(2)]+1

5=5

Answer 2

 Straight line is the shortest distance between 2 points.

 

   Knowing coordinates of 2 points or one point and slope, then everything about the line is known

 

  For graph you can just simply connect the line segment, and extend, then coordinate of any point with having one of them known  can be found.

 

 To write the equation Y= mx +b , first evaluate slope, then fit coordinate of one point and evaluate the Y intercept.

  Here:

 

       ( 2, 5 )   ( 4,9)

 

      m = (9-5) / ( 4-2) = 2

 

  Write the equation of the line:

 

     Y = 2X + b

 

    Plug in ( 2,5 ) evaluate b

 

        5 = 2( 2) +b     b =1

 

      So the equation:

      Y = 2X +1

 

      Plug in ( 4, 9) will give the same answer.

 

      If you make the system of equation:

 

      5 = 2m + b

      9 = 4m + b

      You will come up with m=2 b=1    

    

Answer 3

The equation of a straight line is given by:

 

y = mx + b

 

Where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).  You have already figured out what m, the slope, equals. All you need to get the full equation is the value of b.  You can find b as follows:

 

b = y - mx

 

Plug in either of the two points provided for x and y, (2,5) and (4,9), to get b.  Now you have the equation of a straight line.