How To Write a Function Rule Given a Data Table | Algebra

TL;DR

Learn how to write a function rule from a table by identifying the type of function, calculating the slope, determining the y-intercept, and creating the equation.

Transcript

write a function rule given the table shown below so how can we do this well first we need to establish what kind of function we have and looking at the the numbers for x and y we could see it's a linear function whenever x increases by one y increases by three so because we have a constant change for y for every constant change for x we know we're... Read More

Key Insights

• 💱 The type of function can be determined by observing a constant change in y for every change in x.
• 💱 The slope is calculated by dividing the change in y by the change in x.
• ❣️ The y-intercept is found by identifying the y-value when x is 0.
• 😃 The function rule equation is y = mx + b, with m as the slope and b as the y-intercept.
• 😥 Testing the equation with known points from the table helps ensure its accuracy.
• ☠️ Linear functions have a constant slope, while non-linear functions exhibit varying rates of change.
• 💱 When the change in y is positive and the change in x is positive, the slope is positive.

Questions & Answers

Q: How do you determine the type of function from a table?

You can identify if the function is linear by observing a constant change in y for every change in x.

Q: What is the slope and how do you calculate it?

The slope is the change in y divided by the change in x. It represents the rate at which y changes when x increases by one unit.

Q: What is the y-intercept and how do you find it?

The y-intercept is the y-value when x is 0. You can find it by locating the point where the line intersects the y-axis.

Q: How do you create the function rule equation?

Using the slope-intercept form, the equation is y = mx + b, where m represents the slope and b represents the y-intercept.

Summary & Key Takeaways

• To write a function rule from a table, first determine if the function is linear by observing the constant change in y for every change in x.

• Calculate the slope by finding the change in y divided by the change in x.

• Determine the y-intercept by identifying the y-value when x is 0.

• Use the slope and y-intercept to create the function rule equation.