Q.1 (a) Consider the liner equation 3x  - 6y  = 24, determined the following

            (i) What is the slop of any line parallel to the given line

            (ii) What is the slop of any line perpendicular to the given line

            (iii) Fine the equation of line parallel to x-axis and which pass through (2,5)

           

            (b) A publisher received from a printing agency 0f Rs 45,000 for printing 1000 copies of a book and Rs 75,000 for 2,000 copies respectively. Assumed the cost of ‘Y’ increase (y related to x  the number of books printed (a) write the co-ordination of the given proms  (b) write the equation of the line.
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1 Answer

a) i) 3x-6y=24 can be reduced to x-2y=8, 2y=x-8, y=½x-4, which has a slope ½ as does every parallel line.

ii) Perpendicular slope is -2 (-1/½)

iii) y=5 is parallel to the x-axis and all x values are on this line

b) Linear relation y=mx+a where m is the slope and a is a constant. m=(75000-45000)/(2000-1000)=30000/1000=30. a) coords are (1000,45000) and (2000,75000).

Using slope-intercept:

y-45000=30(x-1000), y=30x-30000+45000=30x+15000. Note that when x=2000, y=75000 which confirms the equation as correct:

b) y=30x+15000 where y is revenue in Rs and x is the number of books.

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