To find the equation of the linear function represented by the table, we need to identify the slope (m) and the y-intercept (b) of the linear equation in the form \( y = mx + b \).
Given the x and y values from the table:
| x | y | |---|----| | 0 | -2 | | 1 | 6 | | 2 | 14 | | 3 | 22 | | 4 | 30 |
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Identify the slope (m): The slope can be calculated using any two points from the table. Let’s use the first two points (0, -2) and (1, 6).
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-2)}{1 - 0} = \frac{8}{1} = 8 \]
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Identify the y-intercept (b): The y-intercept is the value of y when x = 0. From the table, when \( x = 0 \), \( y = -2 \). Therefore, b = -2.
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Write the equation: Now we have the slope \( m = 8 \) and the y-intercept \( b = -2 \). We can write the equation as follows:
\[ y = 8x - 2 \]
Therefore, the equation of the linear function in slope-intercept form is:
\[ \boxed{y = 8x - 2} \]