01SEP21WED

Observation: At every point on the X-Axis, the Y-Coordinate is zero.

Therefore y=0 is the equation of X-Axis.

Similarly, x=0 is the equation of Y-Axis.

[An equation is a mathematical statement that describes the behaviour of a line or curve in space.]

What is the equation of Origin?

Equations exist for lines or curves, not for points.

(-1,-1), (0,0), (2,2), (5,5) are points on a line. What is its equation?

Pattern: At every point on this line, the x-coordinate and the y-coordinate are equal.

Therefore, the equation of the line is y=x.

(1,2), (2,4), (3,6) are points on a line. What is its equation?

Pattern: If x-coordinate is multiplied by 2, we get the y-coordinate.

2 times x is y.

y=2x is the equation of the line.

(1,-1), (4,-4), (0.5, -0.5) are points on a line. What is its equation?

Pattern: If x is negated, we get y.

y = -x is the equation of the line.

(4,2), (8,4), (14,7) are points on a line. What is its equation?

Pattern: x over 2 equals y, or, y multiplied by 2 gives x.

y=x/2 or 2y=x

(1,3), (2,5), (3,7), (4,9), (5,11) are points on a line. What is its equation?

Pattern: Double x and add 1. You get y.

y = 2x+1

(1,5), (2,8), (3,11), (4, 14) are points on a line. What is its equation?

Pattern: x multiplied by 3 and 2 added to it gives y.

y = 3x+2

(5,13), (4,10), (3,7), (2,4) are points on a line. What is its equation?

Pattern: x multiplied 3 and 2 subtracted from it gives y.

y = 3x-2