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



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how to find the slope of line ax+by = c


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).

Thanks for devoting your precious time to this post How to find the slope of line when its equation is given,ax+by=c calculator, ax+by+c=0, meaning,ax+by+c=0 solve for y, ax+by=c given two points, ax+by=c what is c, slope formula,ax+by=c meaning,slope of a line formula,




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