Learning Intercept Form

Introduction to Learning  intercept  form:

 Slope:

             An area of surface that tends evenly towards top or down is called as slope. The slope is also called as gradient. The slope of a line  containing the x and y axes is generally represented by  m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

 

Learning Intercept form :

 

Slope form:

               The equation of the line can be expressed as the following forms,

 Slope Intercept form:

                 Y=mx+b,

   Where ,

               m=slope

                b=Y-intercept

           An equation for a line with nonzero x-intercepts and 
y-intercepts can be written as:
                        x/a + y/b = 1
          where , a = x-intercept  
                     b = y-intercept.
 This is called the intercept form of the equation of a line.

Learning Point slope form:

                  (y-y1)=m(x-x1),

         Where, m=slope and

               (x1,y1 ) are the points that lies on the line.

Slope form:

                  Slope m= (y2-y1)/(x2-x1)

                                            Or

                            m= (y1-y2)/(x1-x2)

 Where (x1, y1) and (x2, y2) are the two point’s lies on the line.

 

learning intercept form- Slope of Parallel and Perpendicular intercept lines:

 

1. Parallel lines have equal slope.

    (That is if m1 is slope of line1 and m2 is slope of line2, then    m1=m2)

2. Perpendicular lines have negative reciprocal slopes.             

    (That is if m1 is slope of line1 and m2 is slope of line2, then m1=-1/m2)

Learning - Sample slope intercept form problems:

 1. Find the slope of the equation y=4x-3

        Solution:

                      Y=4x-3

                       It is in the slope intercept  form y=mx+b.

                           So slope of the given equation m= 4

 2. Find the slope- intercept  of the equation 3y=6x-12

   Solution:

                 3y=6x-12

                  Divide by 3 on both sides,

                  Y=2x-4

                  So slope –intercept of the given equation b= -4

3. Find the slope -y=3x+7

    Solution:

                  -y=3x+7

                   Divide by -1 on both sides,

                   Y=-3x-7

                    So slope of the given equation b= -7

4. Verify the below equations are parallel.

                             4y=16x+12

                             Y=4x+8

                             Divide by 4 on both sides,

                             Y=4x+3

                             Slope m1=4

                             The slope of the second equation is m2=4

                             m1=m2=4

                              So both equations are parallel.

5.find the intercept of the given equation : x / 8 + y / 5 = 1

       Solution:

             x/a + y/b = 1
    where , a = x-intercept  
               b = y-intercept.
         So, x-intercept   = 8
               y-intercept   = 5