In the `xy`-plane, the graphs of the equations `y = x^2 + x - 2` and `y = 5x - 5` intersect at two distinct points. Wha…

To find the intersection points of the two graphs, set the expressions for `y` equal to each other:

`x² + x - 2 = 5x - 5`

Next, rearrange the equation into the standard quadratic form `ax² + bx + c = 0`. Subtract `5x` from both sides and add `5` to both sides:

`x² + x - 5x - 2 + 5 = 0`

`x² - 4x + 3 = 0`

Now, solve the quadratic equation for `x`. This equation can be factored. We need two numbers that multiply to 3 and add up to -4. These numbers are -1 and -3.

So, the factored form is:

`(x - 1)(x - 3) = 0`

The two possible values for `x` are `x = 1` and `x = 3`. These are the `x`-coordinates of the two intersection points.

The question asks for the `x`-coordinate of the point with the greater `y`-coordinate. We need to find the `y`-coordinate for each `x`-value using one of the original equations. Using the linear equation `y = 5x - 5` is simpler.

For `x = 1`:

`y = 5(1) - 5 = 5 - 5 = 0`. The intersection point is (1, 0).

For `x = 3`:

`y = 5(3) - 5 = 15 - 5 = 10`. The intersection point is (3, 10).

Comparing the two points, (1, 0) and (3, 10), the point with the greater `y`-coordinate is (3, 10). The `x`-coordinate of this point is 3.

Therefore, the correct answer is 3.

A is incorrect. This is the `x`-coordinate of the other intersection point, (1, 0), which has the smaller `y`-coordinate.

C is incorrect. This is the `y`-coordinate of the intersection point (1, 0).

D is incorrect. This is the `y`-coordinate of the correct intersection point, (3, 10), but the question asks for the `x`-coordinate.