Slope =m = (y

_{2}-y

_{1})/(x

_{2}-x

_{1}),

Where ‘x

_{1}’, ‘x

_{2}’ are the co-ordinates of X- axis,

And ‘y

_{1}’, ‘y

_{2}’ are the co-ordinates of Y- axis,

Let’s take an example:-

If we have ‘X’ co-ordinate (1, 4) and ‘Y’ co-ordinates (5, 3) than in that case by using the formula of slope,

Slope = m = (y

_{2}- y

_{1}) / (x

_{2}- x

_{1}),

So by putting the values of co-ordinates

m = (5 - 3)/ (1 - 4),

m=-2/3.

So the slope between these axis is -2/3.

If we talk about slope according to Algebra and we have a linear equation which have a slope than formulate linear equation in terms of slope,

Y = mx + b,

Now we have to calculate the value of ‘b’ because the value of slope ‘m’ is known to us. After that rewrite the equation,

b = y – mx,

Now we assume the two points (1, 2) in the above equation,

b=2 - (5 * 1),

And therefore the value of b = 1.5.

Here ‘b’ is also the y- axis intercept which is the value of ‘y’ where the equation term intersects the y- axis. To cross check again we assume other points (5, 4) and we have to find out the value of ‘b’ so by putting these co-ordinates on the above equation.

b = 4 - (.5 * 5),

b = 1.5,

So according to the value of the linear equation is,

y = .5x + 1.5,

To understand it more deeply we take an example where we have a line and the slope of that line is 9 which passes through the co-ordinate (7, 5) and we have to write the equation for that so according to the above formula,

b = y – mx,

b = 5 – 9 * 7,

b = -58,

By putting the value of ‘b’ in standard form of linear slope equation.

y = 9x – 58,

So it is necessary while finding a slope that co-ordinates should be given to us.