Final answer:
The equation of the line passing through (2, 3) and (6, 5) in slope-intercept form is y = (1/2)x + 2, found by first calculating the slope and then using one of the points to solve for the y-intercept.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b, we need to find the line's slope and the y-intercept. The slope (m) is the rise over run, or the change in y over the change in x. For the points (2,3) and (6,5), the slope is calculated as (5 - 3) / (6 - 2) = 2/4 = 1/2.
Next, we use the slope and one of the points to find the y-intercept (b). By substituting into the slope-intercept form:
y = (1/2)x + b
Using point (2, 3), we get:
3 = (1/2)(2) + b
3 = 1 + b
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = (1/2)x + 2.