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

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(2,5)$ and $(x_2,y_2)=(6,9)$. So $m=\frac{9 - 5}{6 - 2}=\frac{4}{4}=1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(2,5)$ and $m = 1$, we have $y - 5=1\times(x - 2)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 5=x - 2$. Then add 5 to both sides to get $y=x+3$.

Answer:

A. $y=x + 3$