In coordinate geometry, the slope of a line is a measure of its steepness and direction. It is represented by the letter “m” in the equation of a line, y = mx + b. The slope of a line can be positive, negative, zero, or undefined. A positive slope indicates that the line is rising from left to right, a negative slope indicates that the line is falling from left to right, a zero slope indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.

The slope of a line can be found using the rise over run method, which involves finding the ratio of the change in y to the change in x for any two points on the line. It can also be found by using the formula: m = (y2 – y1) / (x2 – x1)

In real-world applications, the slope of a line can be used to determine the rate of change of a quantity. For example, in economics, the slope of a line can be used to determine the elasticity of demand for a product. A steep slope indicates that the quantity demanded changes a lot for a small change in price, while a shallow slope indicates that the quantity demanded changes very little for a small change in price.

Another example is in construction, the slope of a line can be used to determine the angle at which a surface should be inclined. For example, a slope of 1/8 is often used for wheelchair ramps, as it is a moderate incline that is easy to navigate for people with mobility impairments.

To find the slope of a line, we can use the formula: m = (y2 – y1) / (x2 – x1). Let’s take an example, find the slope of the line represented by the equation y = 2x + 3

We can pick two points on the line, say (1,5) and (3,9)

m = (y2 – y1) / (x2 – x1) = (9 – 5) / (3 – 1) = 4/2 = 2

So the slope of the line represented by the equation y = 2x + 3 is 2

In conclusion, the slope of a line is a measure of its steepness and direction, it can be positive, negative, zero or undefined, it can be calculated by using the rise over run method or by using the formula (y2 – y1) / (x2 – x1). The slope of a line has many real-world applications, such as determining the rate of change of a quantity and determining the angle of incline for surfaces in construction.