Question

The line through A(2,y) and B(-1,8) whose slope is -2. What is y?

Answer 1

The slope is just the proportion of the "how much you de-/ascend, when you make a step in one direction". This is why you have to substract the secound entries from each other, to get the difference in hight between your points. to get the proportion right, you finally have to know, how many steps you went in the "plane direction" by substracting the first entries and dividing by them.

So, the answer to your problem is: you have to calculate the slope. Again: you do this by subtracting the second entries of the points A and B and then devide by the difference of the first entries of A and B.
Let's say A=(A1,A2), B=(B1,B2) so that A1=2, A2=y, B1=-1 and B2=8
\[slope= \frac{ A2-B2 }{ A1-B1 }\] Most parts of this equation, we already know, so that:\[slope= -2=\frac{ y-8 }{ 2-(-1) }= \frac{ y-8 }{2+1}=\frac{y-8 }{ 3 }=-2\] So know we can directly calculate y by multiplicating with 3 and adding 8 on both sides of the equation :\[-2*3+8=y\] And finally:\[y=2\]