What you’ll learn
Identify proportional relationships from graphs.
Key idea
Its slope is the constant of proportionality k, so points on the line have the same output-to-input ratio. A straight line that crosses the vertical axis somewhere other than zero is linear but not proportional.
When reading a graph, check its axes and scale before comparing coordinates. Pick two nonzero points and calculate y/x for each. The ratios should match. The origin condition matters too; a line can have a constant slope and still include a starting amount.
Worked example
Enter the exact value or ordered values in the format requested below.
Read the constant y/x from this straight graph, x horizontal and y vertical.
Marked coordinates: P=(2, 10); P=(1, 5); P=(0, 0).
- The straight graph passes through the origin.
- At the nonzero point (2,10), y/x=10/2=5; all shown points follow y=5x.
Answer: 5
Quick Check
Relate the graph used in 'Identify proportional relationships from graphs' to an equation, table, transformation, or verbal description.
Connect the straight graph to a proportional equation with evidence from origin and nonzero points.
Marked coordinates: P=(2, 6); P=(1, 3); P=(0, 0).