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# distance between curve and line question thing watch

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1. (im terrible with titles to my threads lmaooo)

hey guys
i need help with this question, ive thought about a variety of different ways to try and determine the answer, through integration or setting the equations equal to one another or even using Pythagoras to try and solve this, but to no luck unfortunately!

how is a question like this supposed to be approached? I've used Desmos to see the graphs and without gettin too technical with the numbers, visually it appears the two graphs are closest where the curve is one unit deep (giving the point 1,5). however, when i tried solving what x would be when y = 5 for 5x-6, i do not get any of the answers available in the multiple choice

any help would be greatly appreciated! thanks Attachment 693932693934
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2. The question does not involve integration at all. What's the logic behind the working that you've done so far?
3. (Original post by B_9710)
The question does not involve integration at all. What's the logic behind the working that you've done so far?
to be honest i don't really know what im doing, the working out is just random attempts to try and attain the answer. im not sure how to find the two closest points on each line
4. You're finding the shortest vertical distance between the line and the curve.The vertical distance between the line and the curve will be given by the value of the y coordinate of the curve - the value of y coordinate of the line.
Let us denote this distance function by which you should be able to see is given by .
Now you're finding the minimum value of this function - which you should know how to do - it's a quadratic function.
5. (Original post by B_9710)
You're finding the shortest vertical distance between the line and the curve.The vertical distance between the line and the curve will be given by the value of the y coordinate of the curve - the value of y coordinate of the line.
Let us denote this distance function by which you should be able to see is given by .
Now you're finding the minimum value of this function - which you should know how to do - it's a quadratic function.
ahh thank you very much! that made perfect sense and i understand this now, and also ended up getting the right answer, thank you

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