Final answer:
The equation is y = (1/6)x + 19/24.
Step-by-step explanation:
To write an equation of the line that passes through the points (5/4,1) and (-1/4,3/4), you need to find the slope ('m') of the line and its y-intercept ('b').
The slope of a line that goes through two points (x1, y1) and (x2, y2) can be found with the formula m = (y2 - y1) / (x2 - x1).
Substituting the given points into this formula, we get m = (3/4 - 1) / (-1/4 - 5/4)
= (-1/4) / (-3/2)
= 1/6.
Now that we have the slope, we can use one of the points to find the y-intercept using the equation y = mx + b.
Let's use the point (5/4,1): 1 = (1/6)(5/4) + b, which simplifies to b = 1 - (5/24) = 19/24.
The equation of the line is therefore y = (1/6)x + 19/24.