Surely, to create an equation of the line that passes through a specific point with a specific slope, we could use the point-slope formula of a straight line, which is:
y - y1 = m*(x - x1)
In this formula, (x1, y1) is a point on the line and m represents the slope of the line.
As per the question, we know that our point (x1, y1) is (3, 2) and our slope 'm' is 1/4.
We substitute these given values into our point-slope equation:
y - 2 = 1/4 * (x - 3)
So, the equation of the line that passes through the point (3, 2) with a slope of 1/4 is: y - 2 = 1/4 * (x - 3).
This is how we can derive the equation of a line when we have a point through which line passes and the slope of the line.
This equation tells us that for any point (x, y) on this line, the relationship y - 2 = 1/4 * (x - 3) will hold true.