answer the questions using the table
x y
-2 80
-1 70
2 40
5 10
the rate of change =___________
the y-intercept =________________
the equation of the line is ________________
To find the rate of change, we can examine the change in y divided by the change in x between any two points.
From -2 to -1, the change in y is 70 - 80 = -10, and the change in x is -1 - (-2) = 1. The rate of change is -10 / 1 = -10.
From -1 to 2, the change in y is 40 - 70 = -30, and the change in x is 2 - (-1) = 3. The rate of change is -30 / 3 = -10.
From 2 to 5, the change in y is 10 - 40 = -30, and the change in x is 5 - 2 = 3. The rate of change is -30 / 3 = -10.
As we can see from the three examples, the rate of change between any two points is always -10, regardless of which two points are chosen.
The y-intercept is the value of y when x is 0. Looking at the table, we can see that when x is 0, y is not given. Therefore, we cannot determine the y-intercept from the given information.
Since the rate of change is constant, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is one of the points on the line.
Let's use the point (-2, 80):
y - 80 = -10(x - (-2))
y - 80 = -10(x + 2)
y - 80 = -10x - 20
y = -10x + 60
Therefore, the equation of the line is y = -10x + 60.