Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the linear function that passes through the points (0, 1/2) and (1, 1/4), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

Where (x1, y1) is one of the points on the line, and m is the slope of the line.

The slope of the line can be found using the two given points:

m = (1/4 - 1/2) / (1 - 0)
m = (-1/4) / 1
m = -1/4

Now, we can choose either of the two points to plug in to find the equation of the line. Let's use the point (0, 1/2):

y - 1/2 = -1/4(x - 0)
y - 1/2 = -1/4x

By simplifying, we get:

y = -1/4x + 1/2

So, the equation that represents the linear function is y = -1/4x + 1/2.