what is slope-intercept form?

Question

I was just wondering, what is slop intercept form and how do you find it?

Answer 1

"y = mx + b" is the slope-intercept form of the equation for any straight line.

 

m = slope

 

b = intercept (i.e., the y-intercept, where x=0).

 

Note: the x-intercept is −b/m.

Answer 2

 All 3 forms of the linear equation are representing different way of the same thing, by moving around the variable.

 

  The whole episode stems from a geometric premise ( postulate), that

 

   Line is the location of points with equal slope:

   

    In a rectangular coordinate System, slope defies as

 

     Difference between Vertical coordinate of 2 given points / over the difference between X coordinates of the same points.

  

   So if coordinates of 2 points is known, then slope can be determined too.

 

     i.e.

          A ( 3, 5 )  , and B ( 1, 7)

 

         Slope m =  ( 7 -5 ) / (1 -3 ) = 2/ -2 = -1

 

          Now , knowing that if we connect by straight edge these 2 points and extend we get a straight line 

 

           We know that all points located on that line have the same slope, the difference between Y coordinate / over the difference between X coordinates is equal -1.

 

     If we place last statement into algebraic statement, represent  the coordinates by:

 

     ( X , Y )   , then    all those points:

 

        ( Y - 5) / ( X -3 ) =- 1   and ( Y - 7) / (X -1) = -1

 

         So , the equation of the line ( the relationship between X, Y of all point on that line) is:

 

           Y - 5 = - X + 3

 

           Y = -X + 2  is the equation of that line.

 

           -1  the coefficient of X is always slope of the line

           

             If we let x =0 , Y=2    ( 0, 2 ) is Y intercepts

 

            All line in a plane are either parallel or have a common points of intersect.

 

           All lines except for lines parallel with Vertical and Horizontal axis X = k , Y = m have both Vertical

           and Horizontal intercept points.

 

           In general we write the main geometric Postulate of a line:

 

         ( X , Y )    ( X_{1 ,} Y ₁)    

 

           (Y - Y_{1) / (} X _- X1_{) =} m

 

          So point slope form comes up as

 

          Y - Y_{1 =} m ( X - X₁) / Slope and one point

 

         Now if for ( X_{1 ,} Y _{1 )} we place ( ( 0 , b ) , the Y intercept

 

            Y - b= m ( X - 0 )

     

            Y = mX + b   / Slope intercept form

 

            - mx + Y = b  / Standard point.

 

           Conclusion: If 2 points of a line or one point or slope of a line is known then everything about the

 

            line can be found.

 

 

            

 

         

 

 

 

Answer 3

The standard form of a straight line is:

 

Ax + By = C

 

Where A, B, and C are constants.  The slope-intercept form for a straight line is:

 

y = mx + b

 

Where m is the slope of the line and b is the y-intercept.  To convert from the standard to the slope-intercept form, solve the standard form for y:

 

Ax + By = C

 

By = C - Ax

 

y = (-A/B)x + (C/B) = mx + b

 

Where the slope m = (-A/B) and the y-intercept b = (C/B).