Choosing Appropriate Axis Scales and Origins for Graphing Relations
Grade 9 students in California Reveal Math Algebra 1 learn to choose appropriate axis scales and origin positions so that all ordered pairs in a relation fit clearly on the graph. The process involves finding minimum and maximum x- and y-values, then selecting a scale that spreads points out without leaving large empty regions. For example, a relation with x-values from 2 to 8 and y-values from 5 to 80 works well with a scale of 1 unit per x-grid-square and 10 units per y-grid-square. If negative values exist, center the axes accordingly; if large starting values exist (like x=100,200,300), start the x-axis at 50 rather than 0.
Key Concepts
When graphing a relation on a coordinate plane, choose axis scales and origins so that all ordered pairs $(x, y)$ in the relation fit clearly on the graph. Select a scale (the value each grid unit represents) that spreads the points out without leaving large empty regions, and position the origin so negative values are visible if needed.
Common Questions
How do you choose an appropriate scale for a coordinate graph?
Find the minimum and maximum values for both x and y in your data. Choose a scale that fits all values within the grid while spreading the points out enough to be clearly readable.
What should you do when all data values are large (like x=100, 200, 300)?
Rather than starting the x-axis at 0 and wasting space, begin at a value close to the data (like 50) and use a larger scale such as 50 units per grid square.
When should the axes be moved from the standard position?
If data includes negative values, position the origin so that negative coordinates are visible on the graph. If all values are positive, the origin can remain at the lower-left corner.
What is the problem with a scale that is too large or too small?
A scale too small forces points off the grid. A scale too large crowds all points into one corner, making relationships between values hard to see.
Can you give an example of choosing a good scale?
For the relation {(2,5),(4,20),(6,45),(8,80)}, use scale 1 unit per x-grid-square and 10 units per y-grid-square with origin at (0,0) so all points fit clearly.
Which unit covers choosing axis scales in Algebra 1?
This skill is from Unit 2: Relations and Functions in California Reveal Math Algebra 1, Grade 9.