Question

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Answer 1

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Let's find out the gradient (Slope " m ") of line q ;

$\qquad \sf  \dashrightarrow \:m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$\qquad \sf  \dashrightarrow \:m = \dfrac{4 - 0}{0 - 1}$

$\qquad \sf  \dashrightarrow \:m = - 4$

Now, since we already know the gradient let's find of the equation of line by using its Slope and one of the points using point slope form of line :

$\qquad \sf  \dashrightarrow \:y - 4 = m(x - 0)$

$\qquad \sf  \dashrightarrow \:y = mx + 4$

Now, plug in the value of gradient ~

$\qquad \sf  \dashrightarrow \:y = - 4x + 4$

here we can clearly observe that, the Area under the curve can easily be represented as :

$\qquad \sf  \dashrightarrow \:y < - 4x + 4$

Since, all the values of y that lies in the shaded region is smaller than the actual value of y for the corresponding values of x in the equation of line q