Which of the following gives an example of a function that is not linear?

Question

options:

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

9x+3y−18=0
9 x plus 3 y minus 18 equals 0

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

2x+3y=16

Answer 1

To determine which of the given options represents a function that is not linear, we need to identify the equations and their forms.

1. \(y = \frac{1}{6}x + \frac{2}{3}\): This is a linear function in the form \(y = mx + b\) where \(m = \frac{1}{6}\) and \(b = \frac{2}{3}\).

2. \(9x + 3y - 18 = 0\): This equation can be rearranged to find \(y\): \[ 3y = -9x + 18 \ y = -3x + 6 \] This is also a linear function.

3. \(y = x^2 - 3x + 2.25\): This equation is a quadratic function due to the \(x^2\) term. Hence, it is not linear.

4. \(2x + 3y = 16\): This can be rearranged to solve for \(y\): \[ 3y = -2x + 16 \ y = -\frac{2}{3}x + \frac{16}{3} \] This is a linear function.

From the analysis, the only function that is not linear is:

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

Answer 2

Which of the following is an ordered pair of the relation y=−2 over 3x+6

Answer 3

To identify an ordered pair from the relation \( y = -\frac{2}{3}x + 6 \), we can substitute any value for \( x \) to find the corresponding value of \( y \). An ordered pair is represented as \( (x, y) \).

Let's calculate an ordered pair by substituting \( x = 0 \):

\[ y = -\frac{2}{3}(0) + 6 = 6 \]

This gives us the ordered pair \( (0, 6) \).

We can also pick other values for \( x \) if required. For example, let’s try \( x = 3 \):

\[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]

This gives us another ordered pair \( (3, 4) \).

In conclusion, two examples of ordered pairs from the relation \( y = -\frac{2}{3}x + 6 \) are:

• \( (0, 6) \)
• \( (3, 4) \)

You can choose any \( x \) value and calculate \( y \) accordingly to find more ordered pairs.