HOW TO FIND SLOPE AND Y INTERCEPT FROM AN EQUATION

The slope-intercept form of a line is :

y = mx + b

where m is the slope and b is the y-intercept.

Slope (m)  =   Rise / Run  =  Change in y/Change in x

The y-intercept is always where the line intersects the y-axis, and will always appear as (0, b) in coordinate form

Example  :

Find the slope and y-intercept of the line whose equation is

(i)  y  =  x+1                    (ii) 5x  =  3y   

(iii) 4x–2y+1  =  0           (iv)  10x+15y+6  =  0

(i)  Answer :

To find slope and y-intercept of the given line we have to compare the equation with slope intercept formula

y  =  mx + b

y  =  x + 1

By comparing, we get

Slope (m)  =  1 and y-intercept (b)  =  1

(ii)  Answer :

5x  =  3y

3y  =  5x+0

y  =  (5/3)x + 0

By comparing, we get

Slope (m)  =  5/3 and y-intercept (b)  =  0.

(iii)  Answer :

4x–2y+1  =  0

2y  =  4x + 1

y  =  (4/2) x + 1/2

y  =  2x + 1/2

y  =  mx + b

By comparing, we get

Slope (m)  =  2 and y-intercept (b)  =  1/2.

(iv)  Answer :

10x+15y+6  =  0

15y  =  -10x-6

y  =  (-10/15)x–(6/15)

y  =  (-2/3)x-2/5

y  =  mx + b

By comparing, we get

Slope (m)  =  -2/3 and y-intercept (b)  =  -2/5.

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