To determine the equation of the linear function that passes through the points (0, 1/2) and (1, 1/4), we start by calculating the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, 1/2) and (1, 1/4):
- \( (x_1, y_1) = (0, 1/2) \)
- \( (x_2, y_2) = (1, 1/4) \)
We plug in the points into the slope formula:
\[ m = \frac{1/4 - 1/2}{1 - 0} = \frac{1/4 - 2/4}{1} = \frac{-1/4}{1} = -1/4 \]
Now we have the slope \( m = -1/4 \).
Next, we use the point-slope form of the line, which can be derived from the slope-intercept form \( y = mx + b \). Since we already know the slope and one of the points, we can use the y-intercept (b) directly, as the function passes through the point (0, 1/2).
Thus, the y-intercept \( b = 1/2 \).
Now we can substitute \( m \) and \( b \) into the slope-intercept form:
\[ y = -\frac{1}{4}x + \frac{1}{2} \]
Now we can match this equation to the options provided:
- Option A: \( y = \frac{1}{4}x + \frac{1}{2} \) (not correct)
- Option B: \( y = -\frac{1}{4}x + \frac{1}{2} \) (correct)
- Option C: \( y = -\frac{1}{4}x - \frac{1}{2} \) (not correct)
- Option D: \( y = \frac{1}{4}x - \frac{1}{2} \) (not correct)
So, the correct answer is:
B. y = -1/4x + 1/2