Question

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

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

Answer 1

To find the equation of the linear function that passes through the points \((0, \frac{1}{2})\) and \((1, \frac{1}{4})\), we can use the formula for the slope of a line, which is given by:

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

Where \((x_1, y_1) = (0, \frac{1}{2})\) and \((x_2, y_2) = (1, \frac{1}{4})\).

Calculating the slope \(m\):

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

Now we have the slope \(m = -\frac{1}{4}\).

Next, we can use the point-slope form of the line equation, which is:

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

We can use the point \((0, \frac{1}{2})\). Plugging in the values into the equation, we get:

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

This simplifies to:

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

Adding \(\frac{1}{2}\) to both sides:

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

Thus, the equation of the linear function that matches the points is:

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

So the correct choice from the options you provided is:

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