Question

VIP at (-2,7) dropped her pass and moved to the right on a slope of -9. Where can you catch up to her to return her VIP pass? I know the answer is (-1 ,-2) my question is how do you solve to get the answer?

Answer 1

we are told that VIP is located at (-2,7) and then she drops her pass. Then she moves on a slope of -9. To determine where you can catch up, we simply analyze what would be the next position by incrementing x by 1.

In this case, we are told that the slope is -9.

Recall that given points (a,b) and (c,d) the slope of the line that joins this points is given by

`m=(d-b)/(c-a)=(b-d)/(a-c)`

Lets call the next point (-1,y) . So using this, we have

`\text{ -9=}\frac{y\text{ - 7}}{\text{ -1 -(-2)}}=\frac{y\text{ -7}}{2\text{ -1}}=y\text{ -7}`

So, by adding 7 on both sides, we get

`y\text{ = -9+7 = -2}`

So, the next position, following a slope of -9 and starting at (-2,7) is (-1,-2)