Try This! (Tables and Graphs)
The linear situation you explored in the last section could be represented by the equation \(y=-2x+5\), where \(x\) represents the number of minutes walking and \(y\) represents your current elevation. According to this equation, after 15 minutes of walking, your elevation is \(-25\), which means that you are 25 feet below the elevation of the center of campus.
The linear equations that you graphed in Lesson 2 modeled a specific situation. Although the context of a problem helps you understand what the answer means, it is not necessary to know the context of the problem in order to graph from an equation. Next, you will create a table and graph and interpret a linear equation without context.
Part 1: Graph
- Complete the data table below by substituting the \(x\)-values from the table into the formula to find the \(y\)-values.
- Use a coordinate plane, like the one below, to graph and connect the ordered pairs from the table in the graph provided.
Example: Use \(x=-5\)
Part 2: Interpret
- Find the slope of this line. What method did you use?
- Explain where you find the slope in the equation \(y=-2x+5\).
- What is the \(y\)-intercept of this line? (Be sure to name the ordered pair.)
- Explain where you find the \(y\)-intercept in the equation \(y=-2x+5\).
Note: The slope-intercept form of a line is given by the equation \(y=mx+b\), where \(m\) represents the slope and \(b\) represents the \(y\) intercept.
Watch the video located at the link below to learn more about graphing lines from equations in the form \(y=mx+b\).