Algebra Question - Power Prep Question

How to go about this question?
do i have to find out intersection points for all the options?
I think there will be a simple way of solving this one. Right?

To start off, where do you think the graph of the line would intersect the given curve? To the left of the y-axis or to the right?

not sure!! I think it can intersect anywhere isn’t?

It cannot intersect to the left of the y-axis because all the given lines have y-intercepts less than 4.

Perhaps the image of all the lines plotted alongside the curve makes it intuitively clear why that is the case.

Consequently, the question becomes:

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Which of the given lines will intersect y = 2x + 4 for x > 0?

A quick slope analysis should enable you to immediately eliminate options A through D.

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sorry I might sound dumb but what’s the role of slope analysis in this question?
though I got your point of visualising the other graphs

Would a line like 2x + 3 intersect 2x + 4? Alternatively, would a line like x + 3 intersect 2x + 4 for x > 0? Looking at the slopes should give you the answer to these questions.

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got it. Thankyouu