Question

Explain how you can find the constant of proportionality from a graph representing a proportional relationship when it shows a point with an x-value of 1 and if it doesn't show an x-value of 1. PLEASE HELP ME I HAVE SUMMER SCHOOL AND NEED THIS DONE ASAP​

Answer 1

Explanation:

To find the value of x^2 + b^2, we can start by solving the given equations.

First, let's rearrange the equation x + b = 2 to solve for x:

x = 2 - b

Now, let's calculate the distance between the points (1, x) and (b, 1) using the distance formula:

Distance = sqrt((x - 1)^2 + (b - 1)^2)

Since the distance is given as 3, we can substitute the values into the equation:

3 = sqrt((x - 1)^2 + (b - 1)^2)

Next, let's square both sides of the equation to eliminate the square root:

9 = (x - 1)^2 + (b - 1)^2

Expanding the equation, we have:

9 = x^2 - 2x + 1 + b^2 - 2b + 1

Simplifying, we get:

9 = x^2 + b^2 - 2x - 2b + 2

Now, let's substitute x = 2 - b into the equation:

9 = (2 - b)^2 + b^2 - 2(2 - b) - 2b + 2

Expanding and simplifying further:

9 = 4 - 4b + b^2 + b^2 - 4 + 2b - 2b + 2

Combining like terms, we get:

9 = 2b^2 - 2b + 2

To find the value of x^2 + b^2, we need to substitute the value of x:

x^2 + b^2 = (2 - b)^2 + b^2

Expanding and simplifying:

x^2 + b^2 = 4 - 4b + b^2 + b^2

Combining like terms, we have:

x^2 + b^2 = 2b^2 - 4b + 4

Therefore, the value of x^2 + b^2 is 2b^2 - 4b + 4.