Find the slope of the line through (1,1) and (x,y) for y=x^2+2 when: (Note: Ensure you carry enough significant digits in your calculation to arrive at an accurate answer.) x= 2.03 x=2+h

To find the slope of the line passing through the points (1,1) and (x,y) for the equation y = x^2 + 2, we need to first find the values of y and then calculate the slope using the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Let's solve the problem step by step:

Step 1: Substitute the given value of x into the equation y = x^2 + 2 to find the value of y.

For x = 2.03:
y = (2.03)^2 + 2
y = 4.1209 + 2
y = 6.1209

Step 2: Now, we have the two points: (1,1) and (2.03, 6.1209).

Step 3: Calculate the slope using the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

Slope (m) = (6.1209 - 1) / (2.03 - 1)
Slope (m) = 5.1209 / 1.03
Slope (m) ≈ 4.9782

Answer: The slope of the line passing through (1,1) and (x,y) for y = x^2 + 2, when x = 2.03, is approximately 4.9782.