To find the slope and y-intercept from the given table of values, we can use the coordinates provided in the table:
| X | Y | |----|----| | -3 | 16 | | -2 | 7 | | -1 | -2 |
Using two points from the table, let's take the points (-3, 16) and (-2, 7) to calculate the slope (\(m\)) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Now, substituting the points into the formula:
Let \( (x_1, y_1) = (-3, 16) \) and \( (x_2, y_2) = (-2, 7) \):
\[ m = \frac{7 - 16}{-2 - (-3)} = \frac{-9}{-2 + 3} = \frac{-9}{1} = -9 \]
Now we have the slope \(m = -9\).
Next, we need to find the y-intercept (b) of the equation of the line in the form \(y = mx + b\). We can use any of the points and substitute \(m\) and the \(x\) and \(y\) values into the equation to find \(b\).
Using the point (-2, 7):
\[ 7 = -9(-2) + b \]
\[ 7 = 18 + b \] \[ b = 7 - 18 = -11 \]
Now we have the slope and the y-intercept:
- The slope is \(-9\)
- The y-intercept is \(-11\)
Using the options provided:
- The slope is G -9
- The y-intercept is B (0, -11)
So, the final answer is:
- The slope is G -9
- The y-intercept is B (0, -11)