Question

does the equation represent a linear function or a nonlinear function?
y = -2.2x + 5³
select from the drop-down menu to correctly complete the statement.
the equation choose... in slope-intercept form, so the equation represents a
choose... function.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear function is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept, and \(x\) is raised to the power of 1.

Step2: Analyze the given equation

The given equation is \(y=-2.2x + 5^{3}\). First, calculate \(5^{3}=125\), so the equation becomes \(y=-2.2x + 125\). Here, the coefficient of \(x\) (the slope \(m\)) is \(- 2.2\) and the y - intercept \(b\) is \(125\). The variable \(x\) has an exponent of 1, which fits the form \(y=mx + b\).

Step3: Determine the type of function

Since the equation is in the form \(y = mx + b\) (slope - intercept form of a linear function) and the highest power of \(x\) is 1, the function is linear.

Answer:

The equation \(\boldsymbol{\text{is}}\) in slope - intercept form, so the equation represents a \(\boldsymbol{\text{linear}}\) function.