. Plane and solid analytic geometry; an elementary textbook. the line is to pass lies on the Y-axis, its coordinates being (0, 5), [7] reduces to y-b = lx, or y = lx + b. [8] This is called the slope form of the equation of a the student derive equation [8] geometricallywithout using equation [7]. Ch. IV, § 28] THE STRAIGHT LINE 39 28. Oblique coordinates. — In deriving equations [7]and [8] we have made use of the fact that the axes arerectangular. A separate demonstration is thereforenecessary in oblique coordinates. Using the same construction and notation as in Art. 26,it is again
. Plane and solid analytic geometry; an elementary textbook. the line is to pass lies on the Y-axis, its coordinates being (0, 5), [7] reduces to y-b = lx, or y = lx + b. [8] This is called the slope form of the equation of a the student derive equation [8] geometricallywithout using equation [7]. Ch. IV, § 28] THE STRAIGHT LINE 39 28. Oblique coordinates. — In deriving equations [7]and [8] we have made use of the fact that the axes arerectangular. A separate demonstration is thereforenecessary in oblique coordinates. Using the same construction and notation as in Art. 26,it is again true that P^K= x — xx and KP = y — yv Butthe triangle KPXP isnot right-angled, and inorder to find the ratiobetween its sides wemust make use of thelaw of the sines. Letthe positive direction ofPXP be taken along theterminal line of the an-gle 7. Then the angleformed by the positive direction of PXP with the positive direction of PXK isalways 7, and the angle formed by the positive directionof KP with the positive direction of PXP is (&)— 7).. Fig. 30. Hence, lg- = !LU!i= si 7 , (See Art. 7) PXK x — xt sin ( = 60°. 3. Find the equation of the straight line through the inter-section of the lines 2 x — 3 y = 4: and 3 x — y = 5, and makingan angle of 120° with the X-axis. 4. What is the slope of the line whose intercept on theY-axis is 5 and which passes through the point (3, — 1) ? 5. What system of lines is represented by the equationy —lx + b if we keep I constant and allow b to vary
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