HOW TO FIND THE SLOPE OF LINE AX + BY = C , SLOPE OF LINE

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How To find the slope of ax +by = c

Given Equation is ax + by = c

Transferring the 1st term  containing ‘x’ to R H S

 by = c - ax 

Dividing by b to find value of  ‘y’

y = c/b - ax/b

y =  -ax/b  + c/b, 

Cancelling the terms which are going to be cancelled

Rewriting the equation compatible to y = mx+c

we get , y = (-a/b)x +c/b

Compare this equation with y = mx+c

The slope of the given equation " ax + by = c " is    m = -a/b

Hence  the slope of given line is -a/b.

Note :-So from this method we can say that slop of any line can be written as -(co eff of x /co eff of y)

How To find the slope of  x- Axis

As we know that ,The equation of X-axis is y=0

Rewriting this equation in standard form of  y = mx+c

y = 0.x + 0,

Comparing it with standard form to get m = 0,

⇒ The slope of x-axis is 0 (Zero)

How To find the slope of  Y-Axis

As we know that ,The equation of X-axis is x = 0

Rewriting this equation in standard form of  y = mx+c

0.y = 1.x + 0,

Comparing it with standard form to get m = 0,

⇒ The slope of y-axis is 0 (Zero)

How To find the slope of 4x +3y = 10

Given Equation is 4x + 3y = 10

Transforming the 1st term which contains ‘x’ to R H S

 3y = 10 - 4x

Dividing by 3 to find value of  ‘y’

   y = 10/3 - 4x/3

⇒  y =  - 4x/3  + 10/3

Rewriting the equation compatible to y = mx+c

we get , y = (-4/3)x +10/3

Comparing this equation with y = mx+c

The slope of the given equation is  m = -4/3

Hence  the slope of given line is -4/3

Note simply by applying the formula ,we can calculate the slope of  this line  -(co eff of x/co eff of y) = -4/3

How To find the slope of 2x -7y = -5

Given Equation is 2x - 7y = -5

Transforming the 1st term  containing ‘x’ to R H S

- 7y = -5 - 2x 

Dividing by -7 to find value of  ‘y’

-7y/(-7) = -5/(-7) - (2/-7)x ,

Cancelling  -ve sign of the num with -ve sign of den,we have

⇒  y =  2x/7  + 5/7

Comparing the above  equation  with y = mx+c

we get , y = (2/7)x +5/7,

The co eff of  'x' on the right hand side is the value of slope

The slope of the given equation is  m = 2/7

Hence  the slope of given line is 2/7

Simply by applying the formula ,we can calculate the slope of  this line  -(co eff of x/co eff of y) = -(-2)/(-7) = 2/7

How To find the slope of √2x +√5y = 5

Given Equation is √2x +√5y = 3

Transforming the 1st term  containing ‘x’ to R H S

√5y = 3 - √2x 

Dividing by √5 to find value of  ‘y’

√5y/(√5) = 3/(√5) - (√2/√5)x ,

Cancelling  -ve sign of the num with -ve sign of den,we have

⇒  y =  - (√2/√5)x +3/(√5)

Comparing the above  equation  with y = mx+c

we get , y = - (√2/√5)x +2/7,

The co eff of  'x' on the right hand side is the value of slope

The slope of the given equation is  m =  - (√2/√5)

Hence  the slope of given line is  - (√2/√5).

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