To analyze the data given in the table and derive the required information, let's first extract the points from the data:
- \((-2, 80)\)
- \((-1, 70)\)
- \((2, 40)\)
- \((5, 10)\)
Step 1: Calculate the Rate of Change (Slope)
The rate of change (slope) \( m \) can be calculated by using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We will use two points from the table, for example, the first and second points: \((-2, 80)\) and \((-1, 70)\).
Here \( (x_1, y_1) = (-2, 80) \) and \( (x_2, y_2) = (-1, 70) \):
\[ m = \frac{70 - 80}{-1 - (-2)} = \frac{-10}{1} = -10 \]
Step 2: Find the y-intercept
Now we have the slope \( m = -10 \). We can use one of the points to find the y-intercept \( b \) using the equation of the line:
\[ y = mx + b \]
We can choose the point \((-2, 80)\):
\[ 80 = -10(-2) + b \] \[ 80 = 20 + b \] \[ b = 80 - 20 = 60 \]
So, the y-intercept \( b = 60 \).
Step 3: Write the Equation of the Line
Using the slope and y-intercept we found, we can write the equation of the line in slope-intercept form \( y = mx + b \):
\[ y = -10x + 60 \]
Summary of Answers
- Rate of change = -10
- y-intercept = 60
- The equation of the line in slope-intercept form is \( y = -10x + 60 \)
3 answers