line gh passes through points (2, 5) and (6, 9). which equation represents line gh?\n○ $y = x + 3$\n○ $y = x…

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points (2, 5) and (6, 9), $x_1 = 2$, $y_1 = 5$, $x_2 = 6$, $y_2 = 9$. So $m = \frac{9 - 5}{6 - 2} = \frac{4}{4} = 1$.

Step2: Use point - slope form

Using point - slope form $y - y_1 = m(x - x_1)$ with point (2, 5) and $m = 1$. We get $y - 5 = 1\times(x - 2)$. Simplify this: $y - 5 = x - 2$, then $y = x - 2 + 5$, so $y = x + 3$. We can also check by plugging in the other point (6, 9) into $y = x + 3$. When $x = 6$, $y = 6 + 3 = 9$, which matches the point.

Answer:

A. $y = x + 3$