![]() ![]() If we want to make \(time\) the subject of the equation, we would have to divide both sides of the equation by 2. Removing the proportional sign and adding the constant of proportionality gives: This means that the constant of proportionality which is linking distance to time is 40 รท 20 = 2. ![]() Look at the time value when the distance is 40, you should be able to see that it is 20. The values on the axes also serve another important purpose as they allow us to discover the constant of proportionality from the graph so that we can describe the relationship using an equation. How can you tell if a GRAPH represents a proportional relationship The graph must form a straight line AND the line must pass through the origin (0,0). If this condition is true and the graph is a straight line then we must have a directly proportional relationship. This means that when one of the variables doubles the other variable also doubles, this is the test for proportionality. Look at the values on both of the axes - when the distance axis is 4 the time axis is 2, when the distance axis shows 8 the time axis shows 4. ![]() However, take note of the scales on the graph, if they do not start at (0,0) or if they are not linear take care. When both of these features are present we know that the two quantities on the graph must be directly proportional. Notice that the graph is a straight line starting from the origin. The graph shows that the distance travelled and the time taken are proportional, but how do we know that? Who can tell me what the fancy word is for Unit Rate in proportional situations What letter do we use Constant of Proportionality. How do we know if a graph represents either direct or inverse proportionality? We look for certain features of the graph and perform some test calculations to help us decide. Illustrating direct and inverse proportion ![]()
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