PAGES 46 & 49, I still dont understand after reading the answers from the back of the book

[quote="carmenr1"]PAGES 46 & 49, I still dont understand after reading the answers from the back of the book[/quote]

I can try to explain question no.16 on page no. 46.

We are given the eq =

y = -0.5x + 2

You know this eq

y = mx + c

From here you can calculate the x-intercept = -c/m (check out page no 111)

As y = -0.5x + 2

so, x-intercept = -2/0.5 = 4 = OB (see figure in book)

also, y-intercept = "c" = OA (see figure) = 2

Hence, area of triangle OAB = 1/2 x OA x OB = 1/2 x 4 x 2 = 4

Now, we have to check for all the eqs and correct answer would be the one where area of triangle OAD is half of area of triangle OAB.

Check eq 1

y = -0.25x + 1

x-intercept = -1/-0.25 = 4 = OD (see fig.)

y-intercept = 1 = OA (see fig.)

Area of triangle OAD = 1/2 x OD x OA = 1/2 X 4 X 1 = 2 which is equal to half the area of triangle OAB, so correct.

At this point you can eliminate the answer choices B and C.

Ok, now you can try next choice 2 or 3 depending on the what answer choices are left.

(to save my time I'm just explaining answer choice 3) :) also it's really tough to type particularly Math :)

Analyse choice 3

we are given y = -x + 2

x-intercept = -2/-1 = 2 = OD (see fig.)

y-intercept = 2 = OA (see fig.)

So, Area of triangle OAD = 1/2 x OD x OA = 1/2 x 2 x 2 = 2 which is equal to half the area of triangle OAB, so correct.

Answer = E