how to find the gradient of a straight line (slope)

THIS VIDEO IS A SHORT TUTORIAL THAT EMPLOYS EASY AND SIMPLE UNDERSTANDABLE METHOD OF FINDING THE GRADIENT(SLOPE) OF A LINE. GRADIENT IS THE RATE OF INCLINATION OR DECLINATION OF A SLOPE. The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right. That is:
Gradient = Rise / Run = Change in y / Change in x = (y2 - y1) / (x2 - x1)
A linear graph on the Cartesian plane shows the line PQ defined by the point P(x1, y1) and Q(x2, y2). The rise and run between the two points is shown.

Note:
The gradient of a straight line is denoted by m where:

m = (y2 - y1) / (x2 - x1)
Example 3
Find the gradient of the straight line joining the points P(– 4, 5) and Q(4, 17).
Solution:
Let (x1, y1) = (-4, 5) and (x2, y2) = (4, 17).m = (y2 - y1) / (x2 - x1) = (17 - 5) / (4 - (-4)) = 12 / 8 = 1.5

So, the gradient of the line PQ is 1.5.



The points P(-4, 5) and Q(4, 17) form a straight line on the Cartesian plane.

Note:
If the gradient of a line is positive, then the line slopes upward as the value of x increases.
Example 4
Find the gradient of the straight line joining the points A(6, 0) and B(0, 3).
Solution:
Let (x1, y1) = (6, 0) and (x2, y2) = (0, 3).

m = (y2 - y1) / (x2 - x1) = (3 - 0) / (0 - 6) = 3 / -6 = - 1/2

So, the gradient of the line AB is - 1/2.





The points A(6,0) and B(0,3) form a straight line on the Cartesian plane.

The gradient of a straight line is the rate at which the line rises (or falls) vertically for every unit across to the right. That is:
Gradient = Rise / Run = Change in y / Change in x = (y2 - y1) / (x2 - x1)
A linear graph on the Cartesian plane shows the line PQ defined by the point P(x1, y1) and Q(x2, y2). The rise and run between the two points is shown.

Note:
The gradient of a straight line is denoted by m where:

m = (y2 - y1) / (x2 - x1)
Example 3
Find the gradient of the straight line joining the points P(– 4, 5) and Q(4, 17).
Solution:
Let (x1, y1) = (-4, 5) and (x2, y2) = (4, 17).m = (y2 - y1) / (x2 - x1) = (17 - 5) / (4 - (-4)) = 12 / 8 = 1.5

So, the gradient of the line PQ is 1.5.



The points P(-4, 5) and Q(4, 17) form a straight line on the Cartesian plane.

Note:
If the gradient of a line is positive, then the line slopes upward as the value of x increases.
Example 4
Find the gradient of the straight line joining the points A(6, 0) and B(0, 3).
Solution:
Let (x1, y1) = (6, 0) and (x2, y2) = (0, 3).

m = (y2 - y1) / (x2 - x1) = (3 - 0) / (0 - 6) = 3 / -6 = - 1/2

So, the gradient of the line AB is - 1/2.





The points A(6,0) and B(0,3) form a straight line on the Cartesian plane.

Видео how to find the gradient of a straight line (slope) канала steve kuul