Solve problems involving the gradient of a straight line

Gradient

10.1

Gradient

	Definition

	Gradient is the degree of steepness.

The steepness of a straight line is determined by its gradient value. The greater the gradient value, \(m\) the steeper the slope of the straight line. The negative or positive gradient value determines the direction of the slope of the straight line.

Gradient is the ratio of the vertical distance to the horizontal distance:



Formula

\(\text{Gradient, }m = \dfrac{\text{Vertical distance}}{\text{Horizontal distance}}\)

Formula of gradient of a straight line on a Cartesian plane:

Formula

(i)

		\(\text{Gradient, }m= \dfrac{y_2 -y_1}{x_2 - x_1}\)

(ii)

		\(\text{Gradient, }m = -\dfrac{\text{y-intercept}}{\text{x-intercept}}\)

Gradient for a straight line:

Types of Gradient



(a)		The value of the gradient is positive.

(b)		The value of the gradient is negative.

(c)		The value of the gradient is \(0\).

(d)		The value of the gradient is undefined \((\infty)\).

10.1

Gradient

	Definition

	Gradient is the degree of steepness.

The steepness of a straight line is determined by its gradient value. The greater the gradient value, \(m\) the steeper the slope of the straight line. The negative or positive gradient value determines the direction of the slope of the straight line.

Gradient is the ratio of the vertical distance to the horizontal distance:



Formula

\(\text{Gradient, }m = \dfrac{\text{Vertical distance}}{\text{Horizontal distance}}\)

Formula of gradient of a straight line on a Cartesian plane:

Formula

(i)

		\(\text{Gradient, }m= \dfrac{y_2 -y_1}{x_2 - x_1}\)

(ii)

		\(\text{Gradient, }m = -\dfrac{\text{y-intercept}}{\text{x-intercept}}\)

Gradient for a straight line:

Types of Gradient



(a)		The value of the gradient is positive.

(b)		The value of the gradient is negative.

(c)		The value of the gradient is \(0\).

(d)		The value of the gradient is undefined \((\infty)\).