Final answer:
The equation that represents line GH passing through points (2,5) and (6,9) is y = x + 3. The correct answer is option (a).
Step-by-step explanation:
The equation that represents line GH passing through points (2,5) and (6,9) is y = x + 3.
To determine this, we can use the formula for the equation of a line in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
Using the given points, we can calculate the slope (m) as (change in y) / (change in x):
(9 - 5) / (6 - 2) = 4 / 4 = 1
Since the slope is 1, the equation is in the form y = x + b. To find b, we substitute the coordinates of one of the given points. Let's use (2,5):
5 = 2 + b
b = 5 - 2 = 3
Therefore, the equation for line GH is y = x + 3.`