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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.

\(\begin{array}{c|c} x & y \\ \hline 2 & -5 \\ p & -14 \\ p+2 & -17 \\ \end{array}\)

 Jul 6, 2020
 #1
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Since the values in the table represent the points in a straight line, let's find the slope:

 

m  =  [ (-17) - (-14) ] / (p + 2) - (p) ]  =  -3 / 2   --->   m  =  -3/2

 

Now, let's find the equation of the line by using the point-slope formula:

 

y - (-5)  /  (-3/2)·(x - 2)   --->   y + 5  =  (-3/2)x + 3   --->   y  =  (-3/2)x - 2

 

For the point  (13, q):  y  =  (-3/2)x - 2   --->   q  =  (-3/2)(13) - 2   --->  q  =  -21.5

 

For the point  (p, 14):  y  =  (-3/2)x - 2   --->   14  =  (-3/2)(p) - 2   --->   p  =  -32/3

 

Left for you to finish ...  

 Jul 6, 2020

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