To find the slope and y-intercept of the linear function represented by the points from the table, we can use the given points \( (0, 1) \) and \( (5, -9) \).
- Calculating the slope (m): The slope formula is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (x_1, y_1) = (0, 1) \) and \( (x_2, y_2) = (5, -9) \):
\[ m = \frac{-9 - 1}{5 - 0} = \frac{-10}{5} = -2 \]
- Finding the y-intercept (b): The y-intercept occurs where \( x = 0 \). From the points provided, we can see that at \( x = 0 \), \( y = 1 \). Therefore, the y-intercept is:
\[ b = 1 \]
Now we can summarize our findings:
- The slope is \( -2 \).
- The y-intercept is \( 1 \).
Thus, filling the blanks:
The slope is -2.
The y-intercept is 1.