To find the rate of change, we can compare the change in y-values with the change in x-values.
From x = -2 to x = 5, the change in x is 5 - (-2) = 7.
From y = 80 to y = 10, the change in y is 10 - 80 = -70.
Therefore, the rate of change is -70/7 = -10.
To find the y-intercept, we can look at the point where the line crosses the y-axis. In this case, the y-intercept is the value of y when x = 0. Looking at the table, we can see that there is no data point for x = 0. Therefore, we cannot determine the y-intercept from the given table.
However, we can determine the equation of the line using the point-slope form. We know the rate of change is -10, and let's choose the point (2, 40) to plug into the equation.
Using the point-slope form: y - y1 = m(x - x1), where m is the rate of change and (x1, y1) is the given point, we have:
y - 40 = -10(x - 2)
Expanding the equation:
y - 40 = -10x + 20
Rearranging:
y = -10x + 60
Therefore, the equation of the line is y = -10x + 60.