Final answer:
To write the equation of the line from the table, the slope (m) is calculated from two points, and the y-intercept (b) is noted where x=0. The equation of the line is y = -2x + 6.
Step-by-step explanation:
To write the equation of the line represented by the given table of values, we first need to determine the slope (m) and y-intercept (b) of the line. From the table, we can pick two points to calculate the slope. For example, using the points (2, 2) and (4, -2), the slope (m) is calculated as follows: m = (y2 - y1) / (x2 - x1) = (-2 - 2) / (4 - 2) = -4 / 2 = -2. The slope of the line is -2.
Next, we use the y-intercept which is the value of f(x) when x=0. From the table, when x=0, f(x)=6, so the y-intercept (b) is 6. Therefore, the equation of the line is y = mx + b, which becomes y = -2x + 6.
To summarize, we determined the slope from the change in y over the change in x between two points and identified the y-intercept directly from the table where x=0. This resulted in the linear equation y = -2x + 6.