Final answer:
The equation of the line in slope-intercept form is y = (1/4)x - 1/2.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need the slope and a point on the line. Given that the slope of the line is 1/4 and it passes through the point (6,1), we can substitute these values into the slope-intercept form equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting m = 1/4 and the point (6,1), we get:
1 = (1/4)(6) + b
1 = 6/4 + b
1 = 3/2 + b
Subtracting 3/2 from both sides, we have:
-1/2 = b
Therefore, the equation of the line in slope-intercept form is y = (1/4)x - 1/2.