Question

Writing  The graph shows a proportional relationship between the variables y and x. Write an equation to model the relationship. Use pencil and paper. Explain how you know there is a proportional relationship if you are given either an equation or a graph.

Question content area right
Part 1
The equation y equals
  
enter your response here models the relationship.

Answer 1

I can’t see the graph you mention — please upload it or tell me two points on the line (for example (x1,y1) and (x2,y2)). With that I’ll give the exact equation.

How to get the equation (step‑by‑step):
1. A proportional relationship has the form y = kx. (k is the constant of proportionality or slope.)
2. From the graph, read any point (x,y) on the line (not the origin). Because the line goes through the origin, k = y/x for that point.
- If you have two nonzero points (x1,y1) and (x2,y2), k = (y2−y1)/(x2−x1). For a proportional line this will equal y1/x1 = y2/x2.
3. Write the equation y = kx using the k you found.

How you know it’s proportional:
- From an equation: it’s proportional if it can be written y = kx (no +b term). If there is a +b with b ≠ 0 it’s not proportional.
- From a graph: it’s proportional if the graph is a straight line that passes through the origin (0,0).

Example:
- If the graph goes through (2,6), k = 6/2 = 3, so the model is y = 3x.