Definitions [4]
The two mutually perpendicular number lines intersecting each other at their zeroes are called rectangular axes or coordinate axes, or axes of reference.
The position of a point in a plane is expressed by a pair of numbers, one concerning the x-axis and the other concerning the y-axis. called co-ordinates.
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x → distance from y-axis (abscissa)
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y → distance from x-axis (ordinate)
A Pictograph is a chart that uses pictures or symbols to represent data. Each picture stands for a specific number of items, making the data easy to understand at a glance.
An equation of the form ax + by + c = 0 represents a straight line and is known as a linear equation.
Formulae [4]
One line has a slope m = tanθ
The other equally inclined line has a slope m = − tanθ
Slopes are equal in magnitude, opposite in sign
When slope and y-intercept are given
y = mx + c
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m = slope
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c = y-intercept (value of y when x = 0)
When two points are given
\[\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\]
When the slope and one point are given
y − y1 = m(x − x1)
Key Points
Sign Convention
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Right of y-axis → +x
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Left of y-axis → −x
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Above x-axis → +y
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Below x-axis → −y
Standard Line Results
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x = 0 → y-axis
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y = 0 → x-axis
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x = a → line parallel to the y-axis
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y = b → line parallel to the x-axis
Quadrant Reminder
| Quadrant | Sign of (x, y) |
|---|---|
| I | (+, +) |
| II | (−, +) |
| III | (−, −) |
| IV | (+, −) |
