Graph of Linear Equations
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. 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.
QMaths Official Online Test Series
Graph of Linear Equations
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Reviewed by Admin
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