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Questions and Answers
Which of the following is an example of a linear function?
Which of the following is an example of a linear function?
- y = |x| + 2
- y = x^2 + 5
- y = 3x^2 - 4x + 7
- y = 2x + 3 (correct)
What is the slope of the line represented by the equation y = 3x - 2?
What is the slope of the line represented by the equation y = 3x - 2?
- 2
- -2
- 3 (correct)
- -3
Which of the following equations does not represent a linear relationship between x and y?
Which of the following equations does not represent a linear relationship between x and y?
- y = -2x - 1
- y = 0.5x - 3
- y = 4x + 2
- y = x^2 + 3x + 1 (correct)
If a linear function has a negative slope, how would the graph of the function appear?
If a linear function has a negative slope, how would the graph of the function appear?
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Study Notes
Linear Functions
- A linear function can be identified by the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
- An example of a linear function is an equation where the highest power of the variable(s) is 1.
Slope of a Linear Function
- The slope of a line represented by the equation y = 3x - 2 is 3.
- The slope of a line can be interpreted as the change in y over the change in x (rise over run).
Non-Linear Relationships
- An equation that does not represent a linear relationship between x and y is one where the highest power of the variable(s) is not 1, such as quadratic or exponential equations.
Graph of a Linear Function with Negative Slope
- If a linear function has a negative slope, the graph of the function would appear to be decreasing from left to right, with the y-values decreasing as the x-values increase.
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