# 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

**Linear Equation**: A linear equation is an equation for a

**straight line. I**t 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
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