A Level Maths modulus question

https://www.quora.com/profile/Bravewarrior/p-164847729
Here is the question with its solution. I am stuck on part c. I got to a=5/4 but have no idea where they got a is greater than 2 from?

https://www.quora.com/profile/Bravewarrior/p-164847729
Here is the question with its solution. I am stuck on part c. I got to a=5/4 but have no idea where they got a is greater than 2 from?

Have you tried sketching y=ax on the graph with a greater than 2.

We know from the eqn of the line y=ax it passes through the origin. If a were to equal 2 it would be PARALLEL to the positive argument of the modulus and not intersect it at all, since the vertex of the modulus curve is at (-4,-5) and our line passes through (-4, -8) so it is always below and parallel to this part of the curve. If a were to equal anything more than 2, at some point the line would intersect this positive argument side of the modulus curve. Hope this helps x

Yess, I 've just done it now and can see why a has to be greater in order for the two graphs to intersect! Thank you 🙂

Tbh, in an exam theyve given you the mod sketch and y=ax just corresponds to putting your pen or ruler at the origin (y intersect) and rotating it (both positive and negative gradient) and getting a feel for where it intersects (or not).