Estimate the instantaneous rate of change for x=2 for

y=x
y=x^2
y=7

the instantaneous rate of change at a point is the slope of the graph at that point.

Your first and last equations are straight lines, which of course have a constant slope. For those just state the slope of the lines.

for the second one : y = x^2

find the y values for x = 2 and x = 2.01
you now have two points, find the slope between those two points and round off

To estimate the instantaneous rate of change at x=2 for a given function, we can use the concept of the derivative. The derivative represents the rate at which a function is changing at a specific point.

1. For y=x:
The function y=x represents a straight line with a slope of 1. Since the derivative of a constant value is always 0, the instantaneous rate of change for y=x at any point is equal to the slope of the line, which is 1.

2. For y=x^2:
To find the derivative of y=x^2, we can use the power rule. According to the power rule, the derivative of x^n is n*x^(n-1). Applying this rule, the derivative of y=x^2 is 2x.

At x=2, substitute the value into the derivative equation:
dy/dx = 2x
dy/dx = 2*2 = 4

Thus, the instantaneous rate of change for y=x^2 at x=2 is equal to 4.

3. For y=7:
Since y=7 is a constant function, its derivative is always 0. Therefore, the instantaneous rate of change for y=7 at any point is 0.

To summarize:
- For y=x, the instantaneous rate of change at x=2 is 1.
- For y=x^2, the instantaneous rate of change at x=2 is 4.
- For y=7, the instantaneous rate of change at x=2 is 0.