Write the negation of the proposition.

Some people don't like walking.

All people do like walking

It might be more grammatically correct to say "all people like walking", but I wanted to include the "do" in there because we can see how the "don't" flips to "do". The "some" flips to "all" as well.

The negation of a statement is the complete opposite in every way. If a friend makes a claim that some people don't like walking, and you can prove that all people do like walking, then this contradicts your friend. The same can be said in reverse: if your friend claims "all people do like walking", then you can counter back with "some people don't like walking". All it takes is one counter-example to prove the claim "some people don't like walking" to be correct. In terms of logic, the word "some" means "one or more".

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer