Slope =m = (y2-y1)/(x2-x1),
Where ‘x1’, ‘x2’ are the co-ordinates of X- axis,
And ‘y1’, ‘y2’ 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 = (y2 - y1) / (x2 - x1),
So by putting the values of co-ordinates
m = (5 - 3)/ (1 - 4),
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.