Question 1099209
<br>I see too many students making mistakes on problems like this because they plug numbers into the slope formula without any care as to whether their answer makes sense.<br>
I think you will like math better if you understand what you are doing, rather than plugging numbers into formulas.<br>
The slope of a line tells you how fast you go up or down as you move left to right along the line.  The given slope of -4 means you go down 4 units every time you move one unit to the right.<br>
So think about walking left to right between the two given points.
The point (-2,r) is to the left of (12,10), so you are starting at x=-2 and moving to x=12.  How far do you move in the x direction?  From -2 to +12, a change of 14.
The slope is -4, so you go down 4 units for each change of 1 in x.  So when x changes by 14, y changes by 14(-4) = -56.<br>
So you went down 56 units from a y value of "r" to a y value of 10.  So what must the value of "r" be? 10+56 = 66.<br>
When you get an answer for a problem like this in this way, you are doing the same arithmetic you would be doing if you plugged the numbers into the slope formula.  But you will have a better understanding of what you are doing... and most likely you will be much less likely to get a wrong answer.