Question
Lorena calculated the slope of the linear function that is represented by the table of values as shown. What did she do wrong
Answers
GPT-4o mini
To determine what Lorena might have done wrong in calculating the slope of the linear function from a table of values, we need to go over the general process for calculating the slope, which is defined as the change in the \(y\)-values divided by the change in the \(x\)-values. The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here are some common mistakes that might have occurred:
1. **Choosing Incorrect Points**: If Lorena chose points that do not correspond to the same pair of \(x\) and \(y\) values, she would calculate the wrong slope. It's essential to ensure that both points come from the same function.
2. **Arithmetic Errors**: Simple arithmetic errors when computing the differences in \(y\) and \(x\) can lead to an incorrect slope. It’s easy to miscalculate especially if the numbers are large or complex.
3. **Using Non-linear Data**: If the data provided wasn't actually linear (i.e., did not form a straight line), then the slope calculated would not represent the entire relationship accurately. Lorena might have assumed the data was linear when it was not.
4. **Confusion Between Points**: In any calculations, it’s possible to accidentally mix up which number is \(x_1\) and which is \(x_2\), or which is \(y_1\) and which is \(y_2\).
5. **Incorrect Formula Application**: Sometimes, a person might misapply formulas related to slope, perhaps using a different formula for a different type of line or curve.
If you provide the specific table of values or details about what Lorena did, I could give a more targeted explanation about her miscalculation!
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here are some common mistakes that might have occurred:
1. **Choosing Incorrect Points**: If Lorena chose points that do not correspond to the same pair of \(x\) and \(y\) values, she would calculate the wrong slope. It's essential to ensure that both points come from the same function.
2. **Arithmetic Errors**: Simple arithmetic errors when computing the differences in \(y\) and \(x\) can lead to an incorrect slope. It’s easy to miscalculate especially if the numbers are large or complex.
3. **Using Non-linear Data**: If the data provided wasn't actually linear (i.e., did not form a straight line), then the slope calculated would not represent the entire relationship accurately. Lorena might have assumed the data was linear when it was not.
4. **Confusion Between Points**: In any calculations, it’s possible to accidentally mix up which number is \(x_1\) and which is \(x_2\), or which is \(y_1\) and which is \(y_2\).
5. **Incorrect Formula Application**: Sometimes, a person might misapply formulas related to slope, perhaps using a different formula for a different type of line or curve.
If you provide the specific table of values or details about what Lorena did, I could give a more targeted explanation about her miscalculation!