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Question 65755: Complete the following: “the slope of a line tells you”…..
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! o.k.i am giving below in detail AND ALSO EDITING THE ANSWER IN THE SITE.
Complete the following: “the slope of a line tells you”…..
THE TANGENT OF THE ANGLE THE LINE MAKES WITH X AXIS GOING IN ANTICLOCKWISE DIRECTION FROM THE X AXIS TO THE LINE.
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LET US TRY TO UNDERSTAND FROM A SITUATION IN NORMAL LIFE .SUPPOSE WE ARE TRAVELING UP A HILL ROAD OR FLY OVER BRIDGE.AS WE TRAVEL A FEW FEET FORWARD,WE GO UP A FEW INCHES.IN NORMAL ENGLISH,WE SAY WE ARE CLIMBING UP A SLOPE.REVERSE HAPPENS WHEN WE TRAVEL DOWN THE HILL OR ROAD.
SOME TIMES IF THE INCLINE IS HIGH, WE FEEL MORE STRAIN.WE CALL THE SLOPE IS TOO STEEP.THAT IS FOR A FEW FEET TRAVELED ,WE GO UP BY MORE INCHES.
IN A LEVEL ROAD,FOR A FEW FEET TRAVELED,WE DO NOT GO UP AT ALL..THAT IS WE DO NOT GAIN IN HEIGHT.
IN A LESS STEEP ROAD , WE GAIN A FEW INCHES HEIGHT FOR A FEW FEET TRAVELED.
IN A MORE STEEP ROAD,WE GAIN MORE INCHES IN HEIGHT FOR THE SAME FEET TRAVELED.
IN THE EXTREME CASE OF A LIFT,WE GAIN AS MANY FEET IN HEIGHT AS WE TRAVEL.
TO GIVE AN ANALYTICAL SHAPE TO THIS , MATHEMATICALLY,SLOPE IS DEFINED.
IT IS THE RATIO OF HEIGHT GAINED TO THE DISTANCE TRAVELED IN "HORIZONTAL" DIRECTION ...REPEAT "HORIZONTAL"DIRECTION..THAT IS NOT THE DISTANCE TRAVELED UP THE INCLINE,BUT THE DISTANCE MEASURED ALONG AN IMAGINARY HORIZONTAL LINE UP TO THAT POINT. IT IS ALSO CALLED TANGENT OF THE ANGLE THE SLOPING ROAD MAKES WITH THE IMAGINARY HORIZONTAL LINE.
LIKE FOR EVERY THING ELSE,WE DEFINE POSITIVE AND NEGATIVE DIRECTIONS.
THE DIRECTION IN WHICH CLOCK NEEDLES ROTATE IS CALLED CLOCKWISE DIRECTION AND THE OPPOSITE DIRECTION IS CALLED ANTICLOCKWISE DIRECTION.
WE START FROM THE STARTING POINT AND AN IMAGINARY (OR REAL) HORIZONTAL LINE AS THE STARTING STAGE AND GO TOWARDS THE FINAL POSITION OR INCLINED LINE IN THE SHORTEST POSSIBLE ROUTE.IF THAT SHORTEST TRAVEL IS IN ANTICLOCKWISE DIRECTION , WE SAY IT IS A POSITIVE ANGLE.IF IT IS IN CLOCKWISE DIRECTION , WE SAY IT IS NEGATIVE ANGLE.BUT WE ALWAYS TRY TO GO IN ANTICLOCKWISE DIRECTION AND MEASURE THE ANGLE IN POSITIVE DEGREES.
HOPE IT IS CLEAR.
SLOPE = HEIGHT GAINED/HORIZONTAL DISTANCE = AB/OA = CALLED TANGENT OF ANGLE AOB
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