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Introduction To Euclid's Geometry

Question
CBSEENMA9002131

The coordinates of the points given in the following table represent some of the solutions of the equation   y equals 3 over 2 space space x space minus 1



Find the missing values. Also find the coordinates of the points where the line cuts x-axis and y-axis. 

Solution

                     straight y equals 3 over 2 straight x minus 1
When x = 2,   straight y equals 3 over 2 left parenthesis 2 right parenthesis minus 1 equals 3 minus 1 equals 2
When y = -4,  -4 =  3 over 2 x minus 1
rightwards double arrow space space space space space space space space space space space 3 over 2 straight x equals negative 3
rightwards double arrow space space space space space space space space space space space space straight x space equals space minus 2
When   y = 8,  8 = 3 over 2 x equals negative 1
rightwards double arrow space space space space space space 3 over 2 straight x equals 9
rightwards double arrow          x  = 6
When   x = -10, y = 3 over 2 left parenthesis negative 10 right parenthesis minus 1 equals negative 16
When  x = 1,   y = 3 over 2 left parenthesis 1 right parenthesis minus 1 equals 1 half
When  y = negative 5 over 2 comma space space minus 5 over 2 equals 3 over 2 straight x minus 1
rightwards double arrow space space space space space space space space space space 3 over 2 straight x equals negative 3 over 2
rightwards double arrow         x = -1
Hence, the completed table is as follows:
fraction numerator straight x space space space space space space 2 space space space space minus 2 space space space space space space 6 space space space space space minus 10 space space space space space space space 1 space space space space space space minus 1 over denominator space space straight y space space space space space space 2 space space space space minus 4 space space space space space space space 8 space space space space space minus 16 space space space space space begin display style 1 half end style space space space space minus begin display style 5 over 2 end style space space space space end fraction
For intersection with x-axis, put y = 0
       therefore space space space space space space space space 0 equals 3 over 2 straight x minus 1

rightwards double arrow space space space space space space space straight x equals 2 over 3
Hence, the point of intersection is  open parentheses 2 over 3 comma space 0 close parentheses.
For intersection with y-axis, put x = 0
therefore    y = -1
Hence, the intersection is (0, -1)