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8 (a) Using the axes below, sketch a graph to represent the statement y is directly proportional to x (b) Using the axes below, sketch a graph to represent the statement y is inversely proportional to x - Edexcel - GCSE Maths - Question 8 - 2021 - Paper 3
Question 8
8 (a) Using the axes below, sketch a graph to represent the statement y is directly proportional to x (b) Using the axes below, sketch a graph to represent the s... show full transcript
Worked Solution & Example Answer:8 (a) Using the axes below, sketch a graph to represent the statement y is directly proportional to x (b) Using the axes below, sketch a graph to represent the statement y is inversely proportional to x - Edexcel - GCSE Maths - Question 8 - 2021 - Paper 3
Step 1
Using the axes below, sketch a graph to represent the statement y is directly proportional to x
Answer
To sketch a graph of the statement "y is directly proportional to x", we can start by noting that this implies a linear relationship between y and x. The formula for direct proportionality can be expressed as:
where k is a constant greater than zero. Therefore, the graph will be a straight line that passes through the origin (0,0) and rises to the right. The slope of the line indicates the proportionality constant k. It's important to sketch this line starting from the origin and extending into the first quadrant.
Step 2
Using the axes below, sketch a graph to represent the statement y is inversely proportional to x
Answer
For the statement "y is inversely proportional to x", the relationship can be described by the equation:
where k is a positive constant. This indicates that as x increases, y decreases, resulting in a hyperbolic curve. In the first quadrant, the graph starts high on the y-axis when x is close to zero and approaches the x-axis but never touches it, forming a curve that moves toward the right. The key features to highlight are that the graph never intersects the axes.