10JUl21

We can find the equation of a line by observing the relationship pattern between the x and y coordinates.

The equation of the line connecting (0,0), (1,1) and (2,2) is y=x.

(In math convention, y is always the LHS of the equation of a line. Also, y and x are written in the lower case.)

The equation of the line connecting (1,-1), (2,-2) (3,-3) is y=-x.

The equation of the line connecting (1,2), (2,4) (3,6) is y=-2x.

The equation of the line connecting (2,1), (4,-2) (6,3) is y=x/2.

The equation of the line connecting (1,3), (2,5) (3,7) is y=2x+1.

The equation of the line connecting (1,1), (2,3) (3,5) is y=2x-1.

The slope of a straight line is the difference between the y-coordinates divided by the difference between the x-coordinates, that is, the height of the ladder above the floor divided by the distance of the foot from the wall.

If the line is imagined as a ladder, the foot of which is at (a,b) and the top is at (c,d), the slope of the ladder is (d-b)/(c-a).

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