The ordered pairs for a linear graph are recorded in the table below.x –2 0 1 2y 4 0 –2 –4What is the algebraic equation for this table of values?
Question
What is the algebraic equation for this table of values?
| x | -2 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | 4 | 0 | -2 | -4 |
Solution
The given ordered pairs are (-2, 4), (0, 0), (1, -2), and (2, -4).
To find the algebraic equation, we need to determine the slope (m) and the y-intercept (b) for the equation in the form y = mx + b.
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Calculate the slope (m): The slope is the change in y divided by the change in x. Using the first two points (-2, 4) and (0, 0), the slope m = (0 - 4) / (0 - (-2)) = -4 / 2 = -2.
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Identify the y-intercept (b): The y-intercept is the value of y when x = 0. From the table, we can see that when x = 0, y = 0. So, b = 0.
Therefore, the algebraic equation for this table of values is y = -2x + 0, or simply y = -2x.
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