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5. A slope 3),; rise point with its slope, also, Plot the points, Draw the straight line through them, Find the slope of the line. (1, 2) and (3, 5). 6. (-3, -4) and (-2, -3). (3, 2) and (-3, -5). 7. (6, 7) and (-3, (0, 5) and (-2, 3) and (2, -2). 8. 2, 0). 2). AN INTRODUCTION TO MATHEMATICS 50 [CHAP. VI 37. Distance between two points, P(x\, y\) and Q(xz, 2/2) in terms of the coordinates of the points. In Fig. 18 we see that PQ = V(PA) 2 + (AQ) 2 . PQ = V(x 2 - *i) 2 + 2 - t/i) 2 PA = X2 x\ and AQ = (7/2 (t/ since Example.

Solve the equations Example. x _ x First Solution. From (1) - = y 4, (1) =- 4y 14. (2) + y. (3) Method. we have = x Substituting this value for x in 4 +y- Substituting 6 for y in x (1), - = 6 we (2), =- 4y -3y = - or 4 14, y 18, find we find 4, or (4) = 6. x = 10. Hence the required values for x and y are 10 and 6 respectively. This method is known as elimination by substitution. Solution. From Second Method. (1) subtract (2) and we get 3y Multiplying (1) by 4 and (4) and (5), Hence the required (2) = y 18, by 6.

This will give any number of pairs of values which may be plotted as coordinates of points. Equation (2) expresses y as a function of x, and the graph of this function It called the graph of equation (1). be easily shown that the graph of is may all equations of the form of (1) is a straight line. It is because of this fact that such equations are called linear equations. When or is zero, the graph is a line parallel to the X-axis A B or to the y-aris respectively. Thus, the equation y 3 = gives a And the equation line parallel to the X-axis, and 3 units above it.

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An Introduction To Mathematics - With Applns to Science and Agriculture by I. Miller


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