SOLUTION: (-5,r) (1,30), m=7/6

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Question 1099832: (-5,r) (1,30), m=7/6
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Use the formula for Slope.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Recall the equation for the slope of a straight line passing through two given points  (,)  and  (,):

m = .


Substitute the given data into this equation


 = .


It is your basic equation.


First simplify it:


 = ,  or,  equivalently,   = .


It implies, after canceling the common denominator 6


7 = 30 - r  ====>  r = 30-7 = 23.

Solved.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The first tutor simply said "use the formula for slope". Not too helpful....

And then the second tutor used the formula for slope and did a lot of work to get the answer.

I would suggest that you will appreciate the mathematics more if, instead of plugging numbers into a formula for slope, you use your UNDERSTANDING of what slope means.

And if you have that understanding, you will get to the answer with much less work than what the second tutor showed.

The slope of a line is the measure of how far you move up or down, compared to how far you move from left to right. So I always picture in my mind (or on paper, if necessary) moving from left to right from one of the given points to the other.

In this problem, the x values of the two points are -5 and 1. From -5 to +1 is a distance of 6; so I moved 6 units to the right in going from the first point to the second.

The problem tells us the slope is 7/6. That means for each 6 we move to the right in x, we move up 7 in y.

And we DID move 6 units to the right going from the first point to the second; so we must have gone up 7.

And the y coordinate of the second point is 30; if we went up 7 to get there, we must have started at 23.

So the y coordinate of the first point is 23; and that is the number we needed to find.

Without all the explanation, here is all the work that is needed to answer this question:

The change in x, from -5 to +1, is 6; the slope is 7/6, so the change in y must be 7; 30-7=23.
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