By I. Miller

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**Extra resources for An Introduction To Mathematics - With Applns to Science and Agriculture**

**Sample text**

This may be done whether the relation can be expressed by an algebraic equation or not. (See Art. ) Let X'X and Y'Y (Fig. 11) be two straight lines meeting at right angles. Let them be tional relations may considered as two number scales having the point of intersection be any point in the plane. as the zero point of each. Let to two lines. Let x represent the From drop perpendiculars A A AN INTRODUCTION TO MATHEMATICS 30 [CHAP. If the distance to F'F, and y the distance to X'X. the left of ', x is considered negative and if A A lies V to below X'X, y is considered negative.

A constant vame). Problem. Given two points P(x\ y\) and Qfa, 2/2) Express the slope of the line joining these points in terms of the coordinates of the points, Fig. 18. , Solution. Drop perpendiculars Slope of PQ to the axes as shown. AQ = PA 7/2 - Then, y\ (1) X2 Xi Thus the slope of a line between two points is equal to the difference of the ordinates of the points divided by the difference of their abscissas subtracted in the same order. In Fig, 18 (a), the slope is positive since both AQ and PA SYSTEMS OP LINEAR EQUATIONS.

Therefore begin at (2, . f means a 3 units and run 5 units to the right. ) (2, 3). final 2. Construct a line through (1, 2) having f for one having f for its slope. For each of the following pairs of points: (a) (6) (c) 3. 4. 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.

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