math
posted by Ron on .
a) What is the area of the triangle determined by the lines y= − 1/ 2x + 5,y =6x and theyaxis?
(b) If b > 0 and m < 0, then the line y = mx +b cuts off a triangle from the first quadrant. Express the area of that triangle in terms ofm andb.
(c) The lines y = mx +5, y = x and the yaxis form a triangle in the first quadrant. Suppose this triangle has an area of 10 square units. Findm.

a)
Find where the two slanting lines intersect:
x/2 + 5 = 6x
x = 10/13
That's the height of a triangle with base on the yaxis, length 5.
Area = 5 * 10/13 = 50/13
b)
the height = b
the width is where y=0: x = b/m
Area = b * b/m = b^2/m
c)
where do they intersect?
mx+5 = x
x = 5/(1m)
That's the height of the triangle with base on the yaxis, length 5
Area = 5/(1m) * 5 = 25/(1m)
25/(1m) = 10
25 = 10m  10
m = 35/10 = 3.5 
a) x/2 +5 = 6x
x=10/13
A= 1/2 (b)(h)
A= 1/2 (10/13)(5)= 25/13
b) height=b
width= x =b/m
A= 1/2 (b/m)(b)= b^2/2m
c) x=5/(1m)
10=1/2 (5) (5/(1m))
m= 1/4