Question

The graph of a linear function passes through the points (0, 1/2) and (1, 1/4).







) and (1,







).



Which equation represents the function?

Responses
A. y = 1/4x + 1/2














B. y = - 1/4x + 1/2














C. y = - 1/4x - 1/2














D. y = 1/4x - 1/2

Answer 1

To find the equation of the linear function that passes through the points (0, 1/2) and (1, 1/4), we can start by calculating the slope (m) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where \((x_1, y_1) = (0, 1/2)\) and \((x_2, y_2) = (1, 1/4)\):

\[
m = \frac{1/4 - 1/2}{1 - 0} = \frac{1/4 - 2/4}{1} = \frac{-1/4}{1} = -\frac{1}{4}
\]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

\[ y - y_1 = m(x - x_1) \]

Using the point (0, 1/2) and the slope \(-1/4\):

\[
y - \frac{1}{2} = -\frac{1}{4}(x - 0)
\]

This simplifies to:

\[
y - \frac{1}{2} = -\frac{1}{4}x
\]

Now, add \(\frac{1}{2}\) to both sides to solve for \(y\):

\[
y = -\frac{1}{4}x + \frac{1}{2}
\]

Thus, the equation can be rewritten as:

\[ y = -\frac{1}{4}x + \frac{1}{2} \]

Looking at the response options provided, we find that the correct equation that represents the function is:

**B. \( y = -\frac{1}{4}x + \frac{1}{2} \)**