Question

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Functions Quick Check
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Question
Which of the following gives an example of a function that is not linear?(1 point)
Responses

2x+3y=16
2 x plus 3 y equals 16

y=1/6 x+2/3
y equals Start Fraction 1 over 6 End Fraction x plus Start Fraction 2 over 3 End Fraction

y=x^2−3x+2.25
y equals x squared minus 3 x plus 2.25

9x+3y−18=0

Answer 1

To determine which of the following equations describes a function that is not linear, we need to identify the equations that do not represent a straight line.

1. **\(2x + 3y = 16\)** - This is a linear equation and can be rewritten in slope-intercept form (\(y = mx + b\)).

2. **\(y = \frac{1}{6}x + \frac{2}{3}\)** - This is also a linear equation in slope-intercept form.

3. **\(y = x^2 - 3x + 2.25\)** - This equation is quadratic due to the \(x^2\) term, which means it does not represent a linear relationship.

4. **\(9x + 3y - 18 = 0\)** - This equation can be rearranged into the slope-intercept form and is also linear.

Based on the analysis, the only equation that represents a function that is not linear is:

**\(y = x^2 - 3x + 2.25\)**.