Question

Which equation is a linear function?

A) y = 2/x + 3
B) y = x/2 - 5
C) y = x² + 7
D) y = 2^x - 1

Answer 1

Option B). The linear function among the options given is B) y = x/2 - 5, as it's the only equation in the standard linear format y = a + bx.

Step-by-step explanation:

The usual form of a linear equation is y = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line. Using this formula, we can identify which equation is a linear function. Now let's examine each of the options:

• A) y = 2/x + 3 is not linear because it contains an x in the denominator.
• B) y = x/2 - 5 is linear because it can be rewritten as y = 0.5x - 5, which is of the form y = a + bx.
• C) y = x² + 7 is not linear because it contains an x squared term.
• D) y = 2^x - 1 is not linear because it involves an exponential function of x.

Therefore, the linear function among the options is B) y = x/2 - 5.