Gradient (Slope) Of Line / Inclination

Gradient is defined as inclination or declination

Slope/Gradient = Verticle Rise/HorizontaL Run

In the following triangle, the gradient of the line is given by:

i. Slope = m = (y_2-y_{1/X2-X1) = Change in Y/Chane in X}

ii. Slope = Verticle Rise/HorizontaL Run

iii. Slope = Change in absicss/Change in Ordinate

iv. Slope = tanθ = a/b = Tangent at specific point = inclination or delination.

Positive & negative Slopes: A positive slope indicates the value of the dependent variable increases as we go left to right.

Negative Slope: A negative slope means that the value of the dependent variable (usually y) is decreasing as we go left to right:

Inclination:

We have a line with slope m and the angle that the line makes with the x-axis is α.

From trigonometry, we recall that the tan of angle α is given by:

tan α = opposite/adjacent