Graph of Linear Equations

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Graph of Linear Equations For SSC CGL Exam: 


Coordinates

Let's recap the concept of ( x, y ) coordinates, illustrated in the following examples.

Example: Plot the following points on a set of coordinate axes

A (2, 3),  B (0, 4),  C (– 2, 3),  D (– 1, – 2),  E (– 3, 0),  F (2, – 4)

graph1

Linear Equation: A linear equation is an equation for a straight line. It can have one or two variables.

How to calculate coordinates and plot straight line graphs.

Gradient: The gradient of a line is a measure of its steepness. 
Intercept: The intercept of a line is the value where the line crosses the y-axis.

The equation of a straight line is y = mx + c, (slope intercept form, most common form)

where, m = gradient and c = intercept (where the line crosses the y-axis).

Example: 

Parallel and Perpendicular lines: 

Parallel lines have the same gradient. i.e. the equations of parallel lines will always have the same  coefficient of x.

In perpendicular lines, Gradient of one line * Gradient of other line = -1
i.e, gradient of one line = -1 / Gradient of other line.

For example, 

parallel lines 
y = 3x - 7
y = 3x 
y = 3x +3

Perpendicular Lines:
y = 3x + 2.
y = -1/3  x + 2

OTHER FORMS OF LINEAR EQUATIONS:


General (or standard) form:

In the general form the linear equation is written as:

Ax + By = C,

where A and B are not both equal to zero.

  • The graph of the equation is a straight line.
  • If A is nonzero, then the x-intercept = C/A.
  • If B is nonzero, then the y-intercept = C/B.
  • The slope of the line is −A/B.
  • Vertical lines, having undefined slope, cannot be represented by this form.


Slope–intercept form

y = mx + b,

where m is the slope of the line and b is the y-intercept (0, b),

Intercept form

x/a + y/b = 1,

where a and b must be nonzero.


The graph of the equation has x-intercept a and y-intercept b.



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Graph of Linear Equations Graph of Linear Equations Reviewed by Admin on 11:34:00 PM Rating: 5
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