Testing solutions to linear equations | Graphing lines and slope | Algebra Basics | Khan Academy

TL;DR

Determine which linear equation can generate a set of given ordered pairs.

Transcript

Some ordered pairs for a linear function of x are given in the table below. Which equation was used to generate this table? So they give us a bunch of data points. When x is 4, y is negative 8. When x is 7, y is negative 20, so on and so forth. And these points have been generated by one of these equations right over here, so let's just see which o... Read More

Key Insights

• ❣️ By substituting x-values and calculating y-values, linear equations can be evaluated.
• 😥 Two points are sufficient to determine a linear equation.
• 😆 The equation y = -4x + 8 satisfies all given ordered pairs.

Questions & Answers

Q: How can we determine which equation was used to generate a set of ordered pairs?

By substituting the x-values of the ordered pairs into each equation and calculating the corresponding y-values, we can identify the equation that generates the given pairs.

Q: Why is the second equation ruled out?

The second equation, y = -2x + 0, does not generate the correct y-value for the second pair. When x is 7, the calculated y-value is -14, while the actual y-value is -20.

Q: How many points need to be satisfied by a linear function to determine it?

Two points are sufficient to define a line. If a linear function generates any two of the given ordered pairs, it will satisfy all of them.

Q: What is the equation that generates the given ordered pairs?

The equation that generates the given ordered pairs is y = -4x + 8.

Summary & Key Takeaways

• The content discusses how to identify the equation that was used to generate a given set of ordered pairs.

• By substitution and calculation, the content evaluates three potential equations and determines which one satisfies all the given pairs.

• The equation that generates the ordered pairs is y = -4x + 8.