Equation of a line:
An equation is called the equation of a straight line if each point on the line satisfies that equation and no other point on the plane satisfies that equation.
General form of equation of a line:
The general form of equation of a line is ax + by + c=0.
Example:
x + y – 3 = 0
2x – 3y + 1= 0
Formulas for equation of a line:
1. Slope – intercept form:
The slope intercept form of a line is y=mx+b,
Where, m = slope of the line and
b = y-intercept of the line.
Example:
Convert the equation of line x + y – 6 =0 into slope – intercept form.
Solution:
Given equation is x + y – 6 = 0
Subtracting x,
y – 6 = -x
Adding 6,
y = -x + 6 = (-1)x + 6 = mx + b,
where m = -1 and b = 6
2. Point – slope form:
The point slope of a line is y-y1 = m(x-x1),
Where (x1,y1) is a point on the line and
m = slope of the line
Example:
Find the equation of line containing the point (-1,2) whose slope is -1.
Solution:
Here (x1,y1) = (-1,2) and m = -1.
The equation of line is,
y-y1 = m(x-x1)
y – 2 = -1(x+1)
y-2 = -x -1
x + y -1 = 0.
3. Intercept form:
The equation of a line in intercept form is x/a+y/b=1
Where a = x-intercept and
b= y-intercept made by the line.
Example:
Find the equation of line making the intercepts 2 and 3 on the x and y axis respectively.
Solution:
Here a= 2 and b = 3.
The equation of line is,
x/a+y/b=1
x/2+y/3=1
3x + 2y = 3
3x + 2y – 3 = 0.
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