What is the slope of the function represented by the table of values below
X |
Y |
---|---|
-2 |
13 |
0 |
5 |
3 |
-7 |
5 |
-15 |
8 |
-27 |
Solution:
The slope of the function represented by the values in the given table can be ascertained by calculating the slope between the points represented by the coordinate values.
1) Let us consider the points (-2, 13) and (0, 5)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (5 -13)/(0 - (-2)) = -8/2 = -4
(2) Let us consider the points (-2, 13) and (3, -7)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-7 -13)/(3 - (-2)) = (-20/5) = -4
(3) Let us consider the points (-2, 13) and (5, -15)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-15 -13)/(5 - (-2)) = -28/7 = -4
(4) Let us consider the points (-2, 13) and (8, -27)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-27 -13)/(8 - (-2)) = -40/10 = -4
(5) Let us consider the points (0, 5) and (3, -7)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-7 -5)/(3 - 0) = -12/3 = -4
(6) Let us consider the points (0, 5) and (5, -15)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-15 -5)/(5 - 0) = -20/5 = -4
(7) Let us consider the points (0, 5) and (8, -27)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-27 -5)/(8 - 0) = -32/8 = -4
(8) Let us consider the points (3, -7) and (5, -15)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-15 -(-7))/(5 - 3) = -8/2 = -4
(9) Let us consider the points (3, -7) and (8, -27)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-27 -(-7))/(8 - 3) = -20/5 = -4
(10) Let us consider the points (5, -15) and (8, -27)
Slope = (y_{2} - y_{1})/(x_{2} - x_{1}) = (-27 -(-15))/(8 - 5) = -12/3 = -4
Hence we see that the slope between any pair of points is -4.
Hence we can conclude that the points lie on the straight line. The equation of the straight line is:
y - (-15) = (-4)(x - 5)
y + 15 = -4x + 20
y = -4x + 5
What is the slope of the function represented by the table of values below
Summary:
The slope of the function represented by the table of values below is -4.
X |
Y |
---|---|
-2 |
13 |
0 |
5 |
3 |
-7 |
5 |
-15 |
8 |
-27 |
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