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Straight Line

Any equation with the degree of equation being one is known as an equation of straight line. General equation of straight line is given by aX + bY + c = 0, where X and Y are variables and abc are constants.
 
Any point lying on this line will satisfy the equation of the line.
 
If AB is a straight line on the XY plane, then the angle q which the line makes with the X-axis in the anti-clockwise direction is called the inclination of the line and tangent of this angle q (tan q) is called the slope of the line AB. It is denoted by ‘m’. The lengths OP and OQ are respectively known as the intercepts on X-axis and Y-axis, made by the line.

Slope-intercept form: Different Forms of a Straight Line

y = mx + c
 
If ‘m’ is the slope of the line and ‘c’ the intercept made by the line on Y-axis, the equation is

y = mx + c
 
Description: 16148.png

Point-slope form: Different Forms of a Straight Line

If 'm' is the slope of the line and it passes through the point, the equation is (x1,y1), then the equation of the line is given by:
 
y - y1 = m(x - x1)

Two-point form: Different Forms of a Straight Line

If the line passes through two points (X1y1) and (X2Y2) the equation is
 
Description: 14162.png
 
Description: 16158.png
 
Using point-slope form and two-point form, we can find out the formula for slope also. Comparing the two equations, we get m = Description: 14169.png

Slope-intercept form: Different Forms of a Straight Line

If the line makes an intercept of a units on X-axis and b units on Y-axis, then the equation is:
 
Description: 14178.png
 
Description: 16171.png

 

Finding Slope of a line:

  1. If equation of the line is ax + by = c, then slope of line = Description: 15391.png
     
    For example, slope of line 2x + 3y = 5 is Description: 15383.png
  2. if two points (x1y1) and (x2y2) are given, then slope of line = Description: 15371.png




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