To analyze the data in the table and answer the questions, we can first identify that we have a set of points:
- \((-2, 80)\)
- \((-1, 70)\)
- \((2, 40)\)
- \((5, 10)\)
1. To find the rate of change (slope):
The rate of change (slope) \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's use the first two points \((-2, 80)\) and \((-1, 70)\):
\[ m = \frac{70 - 80}{-1 - (-2)} = \frac{-10}{1} = -10 \]
Thus, the rate of change is \(-10\).
2. To find the y-intercept:
Using one of the points and the slope, we can express it in point-slope form and then convert it to slope-intercept form \(y = mx + b\).
From our earlier calculation, the slope \(m = -10\). Using the point \((-1, 70)\):
Using the linear equation form: \[ y - y_1 = m(x - x_1) \] Substituting the slope and the point: \[ y - 70 = -10(x + 1) \] Expanding it out: \[ y - 70 = -10x - 10 \] \[ y = -10x + 60 \] So, the y-intercept \(b = 60\).
3. The equation of the line in slope-intercept form \(y = mx + b\):
From our calculations, the slope \(m = -10\) and the y-intercept \(b = 60\). The equation of the line is: \[ y = -10x + 60 \]
Summary of Answers:
- The rate of change = \(-10\)
- The y-intercept = \(60\)
- The equation of the line in slope-intercept form is \(y = -10x + 60\)