+335 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.
\(\begin{array}{c|c} x & y \\ \hline 2 & -5 \\ p & -14 \\ p+2 & -17 \\ \end{array}\)
+23252 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 ...
