a) What is the area of the tri-angle determined by the lines y= − 1/ 2x + 5,y =6x and they-axis?

Question

(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 tri-angle in terms ofm andb.

(c) The lines y = mx +5, y = x and the y-axis form a triangle in the first quadrant. Suppose this triangle has an area of 10 square units. Findm.

Answer 1

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 y-axis, 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/(1-m)
That's the height of the triangle with base on the y-axis, length 5
Area = 5/(1-m) * 5 = 25/(1-m)

25/(1-m) = 10
25 = 10m - 10
m = 35/10 = 3.5

Answer 2

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/(1-m)
10=1/2 (5) (5/(1-m))
m= -1/4