First Year Mathematics

Cover First Year Mathematics
First Year Mathematics
George W Evans
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202. Model A. — Plot the corresponding numbers which satisfy the equation 2x — Sy =6.
In this equation, for any value of x we can obtain a value of y. Thus, if a; = 5, 2 a: = 10, and we have © 10 - -32/ = 6 ® 10 = 3 2/ + 6 ® + 32/ 4 = 32/ ® -6 ® n = y ®-3 Again, if a; = 6, ?/ = 2; if x = —3, y = —4; and so on. Thus we obtain the following table of corresponding numbers: a:= -4, 2/= -4f x = i, y = -n a: = 5, 2/ = U x= -3, ?/= -4 x=%y= -% X = 6, 2/ = 2 a:= -2, y = -H a; = 3, 1/ = a: = 7, 2/ = 2
...f x = 0, 2/= -2 a; = 4, 2/ = 1 X = 8, 2/ = 31 THE LOCUS OF AN EQUATION 175 These pairs of numbers will be represented by the points in Fig. 5, running up toward the right.
Fig. 5.
The Locus of an Equation 203. It would be found, on trial, that all the other pairs of corresponding numbers which satisfy this equation lie on the same line, i. E. , their points fall into line with those already put down. In fact, the straight line drawn through two points that represent any two answers to the equation is a complete list of all possible pairs of corresponding num- bers that satisfy the equation.


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