Final answer:
To tell if an equation represents a linear function, enter your dataset into a calculator to generate a trend line equation. Ensure the equation takes the form y = mx + b or y = a + bx with 'm' or 'b' as the slope and 'a' as the y-intercept, then verify that the graph is a straight line.
Step-by-step explanation:
To determine if an equation represents a linear function with a calculator, you need to recognize that a linear function typically has the form y = mx + b or y = a + bx, where m or b is the slope, and a is the y-intercept. A linear function calculator might require entering data points to generate a trend line, which if produces a straight line, confirms the relationship is linear.
To write the linear equation using a calculator, you'll most likely enter your data points, allow the calculator to calculate the slope (rise over run) and intercept, and then round the equation to four decimal places.
For example, equations like y = x + 4, y = 100(x) + 2,000, and y = 3,000(x) + 500 are all linear because they adhere to the linear equation form and will graph as straight lines.
Conversely, if the equation involves exponents on the variable, sine, cosine, tangent, or other such functions, it does not represent a linear function.
In summary, to analyze the data and conclude whether the association is linear, you should check if, after plugging in your dataset into a calculator, the equation that it provides follows the standard form of a linear function. When the calculated trend line equation meets this criterion, and the graph is a straight line, you can confidently state that the data represents a linear function.