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
9x+3y−18=0
9 x plus 3 y minus 18 equals 0
y=16x+23
y equals Start Fraction 1 over 6 End Fraction x plus Start Fraction 2 over 3 End Fraction
y=x2−3x+2.25
y=x2−3x+2.25
The function that is not linear is "y = x^2 - 3x + 2.25".
To determine whether a function is linear, we need to check if it satisfies the properties of a linear function.
A linear function is one that has a constant rate of change, meaning that the graph of the function is a straight line. The equation of a linear function can be written in the form: y = mx + b, where m is the slope or rate of change and b is the y-intercept.
Let's analyze each of the given options to check if they represent linear functions:
Option 1: 2x + 3y = 16
This equation is in standard form and not in the form y = mx + b. Since it does not have y isolated on one side and x isolated on the other side, it is not a linear function.
Option 2: 9x + 3y - 18 = 0
Similar to the first option, this equation is not in the form y = mx + b. Therefore, it is not a linear function.
Option 3: y = 16x + 23
This equation is in slope-intercept form and represents a linear function. The slope is 16, indicating the rate of change, and the y-intercept is 23, representing the value of y when x is 0. So, this option represents a linear function.
Option 4: y = x^2 - 3x + 2.25
This equation is not in the form y = mx + b. It contains a quadratic term (x^2), which indicates a curved graph. Therefore, it is not a linear function.
Based on the analysis, options 1, 2, and 4 are not linear functions, while option 3 represents a linear function.