To find the slope (m) and the y-intercept (b) of the function represented by the points in the table, we can use the following formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can use any two points from the table. Let's pick the points (-3, 16) and (-1, -2).
- For point 1: \( (x_1, y_1) = (-3, 16) \)
- For point 2: \( (x_2, y_2) = (-1, -2) \)
Now plug in these values into the slope formula:
\[ m = \frac{-2 - 16}{-1 - (-3)} = \frac{-18}{-1 + 3} = \frac{-18}{2} = -9 \]
Now that we have the slope, we can use one of the points to find the y-intercept (b). The slope-intercept form of a linear equation is:
\[ y = mx + b \]
Using the slope \( m = -9 \) and the point (-3, 16):
\[ 16 = -9(-3) + b \] \[ 16 = 27 + b \] \[ b = 16 - 27 = -11 \]
Thus, the slope of the line is \(-9\) and the y-intercept is \(-11\).
Final Answer:
- Slope (m): \(-9\)
- Y-intercept (b): \(-11\)