QQuestionMathematics
QuestionMathematics
Which equation represents a linear function?
y=- 3 x^{2}+ 2 \quad y=- 4 x+ 5 \quad y=x^{3} \quad y= 2 x^{2}
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Answer
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Step 1:: Identify the general form of a linear function
A linear function is of the form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept.
Step 2:: Examine the given equations
For the equation to represent a linear function, it must be in the form $$y = mx + b$$.
Step 3:: Eliminate non-linear functions
- The equation $$y=2 x^{2}$$ is also a quadratic function, so we can eliminate this one.
- The equation y=x^{3} is a cubic function because of the x^{3} term, so we can eliminate this one as well.
Step 4:: Identify the linear function
So, $$y=-4 x+5$$ represents a linear function with a slope of $$-4$$ and a y-intercept of $$5$$.
Final Answer
The equation y=- 4 x+ 5 represents a linear function.
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