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# help

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The points (x, y) represented in this table lie on a straight line. The point (13, q) lies on the same line. What is the value of p + q? Express your answer as a decimal to the nearest tenth. $$\begin{array}{c|c} x & y \\ \hline 2 & -5 \\ p & -14 \\ p+2 & -17 \\ \end{array}$$

Apr 23, 2019

#1
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Hint: They all have the same slope.

Apr 23, 2019
#2
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We can equate slopes to find p

[ - 14 -- 5]       [ -17 - - 5]

________  =__________     simplify

p -  2           (p + 2) - 2

[ -9]             [ - 12 ]

____   =    _______               cross- multiply

p - 2               p

-9p  =  -12 [ p - 2]

-9p  =  -12p + 24         add 12p to both sides

3p  =  24     divide both sides by 3

p = 8

So...the slope   =  -12 / 8   =   -3 / 2

So  since the points ( 2, - 5)  and ( 13, q)   are on the same line....we have....

[q - - 5 ]          -3

_______  =   ___

13  - 2           2

[ q + 5 ]         -3

______  =      ___           cross-multiply

11                2

2 [ q + 5 ]  =  -3 * 11

2q + 10  = -33

2q  =  -43

q = -43 / 2

So p + q  =   8  - 43/2  =    [ 16 - 43 ] / 2  =   -27/2  =   -13.5   Apr 23, 2019