line gh passes through points (2, 5) and (6, 9). which equation represents line gh?\no y = x + 3\no y = x…

Answer:

A. $y = x + 3$

Explanation:

Step1: Find the slope

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

Step2: Use point - slope form

The point - slope form 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

$y-5=x - 2$. Add 5 to both sides: $y=x - 2+5$, so $y=x + 3$.