Let $S$ be the set of lattice points in the coordinate plane, both of whose coordinates are integers between $1$ and $30,$ inclusive. Exactly $300$ points in $S$ lie on or below a line with equation $y = mx.$ The possible values of $m$ lie in an interval of length $\dfrac{a}{b},$ where $a$ and $b$ are relatively prime positive integers. What is $a + b\,?$

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

t hope this

:

option b  

step-by-step explanation:

we know that

the distance from point n to lm in the figure is equal to the distance of the perpendicular line to lm that passes through the point n

so

the distance is equal to the segment no

> given problem

therefore

the distance from point n to lm is equal to

br tat so much r