Introduction of slope in math

In mathematics, the slope or incline of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is

m=`(y2-y1)/ (x2-x1)`

(Source: Wikipedia)

Definition of Constant Slope in Math:

In math, to finding constant slope to build up a slope formula. To begin, we choose points P and Q on the line. To distinguish between the corresponding of these points, we use subscript notation. Point P has coordinates (x1,y1) and point Q has coordinated(x2.y2).

As we move from point P to point Q, the rise is the dissimilarity of the x-coordinates:x2-x1, as the constant slope is the ratio `(rise) / (run)` ,  we have the following formula for calculating constant slope.

In math, another notation that we use to describe constant slope involves the symbol ∆, which is the letter delta from the Greek alphabet. If the modify in y is represented by ∆y and the change in x is represented by ∆x, then:

M=`(Deltay) /(Deltax)` where ∆x≠0

The entire notation associated with the concept of constant slope of a line.

Example for Constant Slope in Math:

In math, find the constant slope of the line passing through (-1,2) and (3,-4)

Strategy we will use the constant slope formula to find the constant slope.

Why?  We  know the coordinates of two points on the line.

Solution:

We can let(x1,y1)=(-1,2) and (x2,y2)=(3,-4). Then we have

m=`(y2-y1)/(x2-x1)` this is the constant slope formula.

=`(-4-2)/(3-(-1))`      substitute -4 for y2, 2 for y1,3 for x2, and -1 for x1.

=`(-6/4)`

=`-3/2`

Write `(-3/2)` with the – sign in front of the fraction. The outcome is negative.

The constant slope of the line is `-3/2`

In math, the line passing through (-1,2) and (3,-4) points. Notice that we obtain the same result when the constant slope of the line is

m=`(rise)/(run)`=`-3/2`