ExplanationLet us assume the line equations in terms of slope

line j: \(y = m1 \times x + c1\) ....... has the point (1,2) on it.

line k: \(y = m2 \times x + c2\) ....... has the point (2,1) on it.

Here m1 and m2 are slopes of the line j and k respectively.

Now putting the values (1,2) and (2,1) respectively into the equations of line j and k... we have

\(m1 + c1 = 2\) and \(2 \times m2 + c2 = 1\)

Let m1 = 5 and m2 = 2 and solve for c1 and c2 from their respective equations

c1 = -3 and c2 = -3

Line j: \(y = 5 \times x -3\)

Line k: \(y = 2 \times x -3\)

Clearly slope m1 is greater.

Now let m1 = 2 and m2 = 5 and solve for c1 and c2 from their respective equations

c1 = 0 and c2 = -9

Line j: \(y = 2 \times x\)

Line k: \(y = 5 \times x -9\)

Clearly slope m2 is greater.

Hence option D is correct.
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Sandy

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