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Athmanand chetu

pls tell me the different ways to find the slope

SAVVEJ

the angle the linemakes with x axis.ie.tan theta =y2-y1/x2-x1

Karthik M

Slope of what? A line, or the tangent to a curve at some point?

Anyway, to find the slope of a line, given its equation, the formula is slope = -x coefficient/y coefficient. So for an equation Ax + By + C = 0
slope = -A/B.

For a curve, to find the slope of the tangent at some arbitary point x, y, simply differentiate the curve equation wrt x and substitute the points x, y in the new equation.

if two points are given, slope of the line connecting the two points is
y2 - y1/x2 - x1.

if two lines are given, slope of one of the two is given, and the angle between the two lines is given, and if u are asked to find the slope of the other line, then use the formula

tan@ = (m2 - m1/1+m1m2)

@ ---> angle between the two lines.

Avinash Sharma

For straight line it is as follows

Given the slope m and "y intercept" b, the equation of the line is

y = m x + b

Given the slope of the line m and one point P₁ = (x₁,y₁) through which the line passes, we can formulate the equation as as:

(y- y₁)/(x-x₁)= m

We have written this equation in a form which makes it clear that the slope calculated between any point (x,y) on the line and the given point P₁ is the same. However, the relationship generally gets simplified algebraically to:

y = m (x-x₁)+ y₁

This form is tidier, but conceals the simple truth behind how the equation was crafted, namely as a statement about the slope of the line.

Given that the line passes through the two points P₁ = (x₁,y₁) and P₂ = (x₂,y₂), we first find that the slope of the line is

slope: m = (y₂- y₁)/ (x₂-x₁)

We can then use the form shown in the second example above---namely,

y = m x + b

Apart from straight line, the most common way of finding slope of the given curve at a given point is to differentiate the equation of curve with respect to independent variable and then find the value at that given point.

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y = m x + b

(y- y1)/(x-x1)= m

y = m (x-x1)+ y1

slope: m = (y2- y1)/ (x2-x1)

y = m x + b

Apart from straight line, the most common way of finding slope of the given curve at a given point is to differentiate the equation of curve with respect to independent variable and then find the value at that given point.

(y- y₁)/(x-x₁)= m

y = m (x-x₁)+ y₁

slope: m = (y₂- y₁)/ (x₂-x₁)