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Sagot :

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

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{4 - 0}{0 - 1}[/tex]

[tex]\qquad \sf  \dashrightarrow \:m = - 4[/tex]

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 :

[tex]\qquad \sf  \dashrightarrow \:y - 4 = m(x - 0)[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = mx + 4[/tex]

Now, plug in the value of gradient ~

[tex]\qquad \sf  \dashrightarrow \:y = - 4x + 4[/tex]

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

[tex]\qquad \sf  \dashrightarrow \:y < - 4x + 4[/tex]

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

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