Decreasing Graphs
Decreasing Graphs is a Grade 7 math topic in Big Ideas Math Advanced 2, Chapter 6: Functions. Students learn to identify decreasing graphs by observing that output values decrease as inputs increase from left to right, showing a negative relationship between variables. Real-world examples include battery life decreasing over time and temperature dropping from noon to midnight.
Key Concepts
When the output values of a graph decrease as we move from left to right, we say the graph is decreasing. A decreasing graph shows a negative relationship between the input and output variables, where larger input values correspond to smaller output values.
Common Questions
What does a decreasing graph look like?
A decreasing graph slopes downward from left to right. As you move along the x-axis to the right, the y-values get smaller. The line or curve goes down.
How do you know if a graph is decreasing?
Trace the graph from left to right with your finger. If the graph goes down as you move right, it is decreasing. The output (y-value) gets smaller as the input (x-value) gets larger.
Give a real-world example of a decreasing relationship.
A phone battery starting at 90% and dropping to 50% over 2 hours shows a decreasing relationship between time and battery percentage. Also, ice melting from 12 lbs to 4 lbs over 4 hours.
Is a decreasing graph the same as a negative slope?
For straight lines, yes. A negative slope means the line decreases from left to right. For curved graphs, decreasing means the y-values fall as x increases, even without a constant slope.