SOLUTION: The points P(2,-3), Q (3,-2) and R (8,z) are collinear, i.e they lie on a straight line. Find the value of z. (give solution not graph and kindly explain)

Question 1126775: The points P(2,-3), Q (3,-2) and R (8,z) are collinear, i.e they lie on a straight line. Find the value of z. (give solution not graph and kindly explain)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
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P(2,-3), Q (3,-2) and R (8,z) are collinear, ...
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slope,

point-slope form:
-

------slope-intercept form

point R(8,z)
z, unknown y-coordinate

Answer by greenestamps(13214) (Show Source): You can put this solution on YOUR website!

I have some comments about the (correct) solution given by the other tutor.

(1) I always strongly recommend that students not find the slope of the line through two given points by plugging numbers into the slope formula. It is far too easy to get the wrong numbers in the wrong places, or to make simple errors in calculations, especially where subtracting a negative number.

You will understand the math better (and therefore enjoy it more!) if you think about what slope means. It tells you how fast you move up or down as you move along the line to the right.

In this problem, to get from the given point P to the given point Q, you move 1 to the right (from 2 to 3) and 1 up (from -3 to -2).

(2) Now, you can use that observation to say that the slope of the line is 1; and you can use that slope and what you know about the coordinates of the other points to solve an equation to find the answer to the question.

But there is no reason to use that value of the slope and some form of an equation for a line to find the answer to the question. Again, you can find the answer far more easily (and understand how you got the answer!) by using your knowledge of what the slope means.

You know that, in going from P to Q, you went 1 to the right and up 1. As you continue to move along the line, you will continue to go up 1 unit for each unit you move to the right.

R is 5 units more to the right from Q; if you are going along the same straight line as from P to Q, then in going 5 units to the right you are going to go 5 units up.

Then, since the y coordinate at Q is -2, the y coordinate at R is -2+5 = 3.

That's a lengthy explanation of the easy and satisfying way to answer the question. Without all the words of explanation, here is all that is involved in solving the problem:

From P to Q: right 1, up 1
From Q to R ("at the same rate"): right 5, so up 5
ANSWER: z = -2+5 = 3
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