Question

Which of the following equations represents a linear function?

x = 3
y equals one half times x minus 5
y equals three fourths times x squared
3x − 6 = 4

Answer 1

The equation that represents a linear function is:

y equals one half times x minus 5

This is a linear equation because it has a constant rate of change, or slope, of one half. This means that for every increase of 1 in x, y will increase by 1/2. The equation is also in the standard form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The other equations are not linear functions:

x = 3 is a vertical line, which is not a function because it fails the vertical line test.

y equals three fourths times x squared is a quadratic function because it includes an x-squared term.

3x − 6 = 4 is a linear equation, but it is not in the standard form of y = mx + b. It can be rearranged to y = (3/1)x - 2, which is a linear equation in slope-intercept form.