Investigation 8: Analyzing and Graphing Relationships
Investigation 8: Analyzing and Graphing Relationships in Grade 4 Saxon Math Intermediate 4 teaches students to identify the rule connecting paired values in a table, write it as an equation, and visualize it on a graph. For example, a table showing hours worked versus amount earned — (1, 15), (2, 30), (3, 45) — reveals the rule multiply x by 15, giving the equation y = 15x. Students learn to check the rule against multiple rows before accepting it, write it symbolically, and understand that the same pattern can be expressed as a table, an equation, or a graph. This builds core algebraic reasoning skills.
Key Concepts
New Concept Now we will learn how to write an equation to represent the relationship in the table.
What’s next Next, you’ll analyze relationships in tables, plot them on coordinate graphs, and write equations to represent the patterns you find.
Common Questions
How do you find the rule from a table of values?
Look at each pair: determine what operation on x produces y. Test the same operation on every pair to confirm consistency. For (1,15), (2,30), (3,45), the rule is y = 15x.
How do you write a relationship as an equation?
Once you identify the rule, express it symbolically. If y is always 15 times x, write y = 15x. Use variables to represent the general pattern.
Why must you check the rule on more than one row?
A rule that works for the first pair might not hold for others. Always verify with at least two additional pairs to confirm the pattern is consistent throughout the table.
How does a graph show the same relationship as a table?
Each row in the table becomes a point on the graph. Plotting all points reveals a visual pattern, often a straight line for rules like y = 15x.
What equation represents earning 15 dollars per hour?
y = 15x, where x is the number of hours worked and y is the total amount earned.