Define Slope

The perception of a slope is central to differential calculus. For non-linear functions, the small change in the rate varies along the curve. The slope or we can say its gradient of line (gradient means the points in the direction of the greatest rate with increase of the scalar field), which describe its steepness, incline or grade and the value which is higher indicates a steeper (that means having the sharp inclination), incline. It is not defined for horizontal or vertical lines.

In the slope of a line we have to follow some of the steps for finding the slope formula for the line.

Step1: – First we find the difference of both the ‘x’ and ‘y’ coordinates. And we have to place both the coordinates in the ratio.

Step 2: – After that we take two points on a line, because we are using two sets of order pair both the coordinates having values ‘x’ and ‘y’.

Step 3: – If a line has a negative slope then it goes down from left to right.

Step 4: – If a line has a positive slope then it goes up from left to right.

Step 5: – IF a line has is vertical then the slope is undefined.

The slope formula for given two points.

The two points are (p1, q1) and (p2, q2)

Then the slope of the line is denoted by ‘m’.

m = rise = change in ‘q’   =   q– q1,

run     change in ‘p’        p–  p1,

Where, the value of (p1 ≠ p2),

In case of algebra, if ‘y’ is the linear function of ‘x’, then the coefficient of ‘x’ is known as slope of the line. If the equation of the line is given by

Y = mx + c; where m is the slope of the line. The line equation is known as slope – intercept form. Now we will see what is the Distance Formula?

The two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:

⇨ d = √ (x2 – x1)2 + (y2 – y1)2. The ICSE class 12 sample papers is very useful for exam point of view.

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