Question

If the correlation of height with age is given by the equation \(y = a + bx\), what would be the nature of the graph?

• A. Straight line
• B. Parabola
• C. Hyperbola
• D. Sigmoid curve

Hint:

y = a + bx is the standard equation of a straight line.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question gives an equation relating height (\(y\)) to age (\(x\)) as \(y = a + bx\), and asks what shape of graph this equation represents.

Step 2: Key Concept:
The general equation of a straight line in two variables is
\[ y = a + bx \]
where \(a\) is the intercept (the value of \(y\) when \(x = 0\)) and \(b\) is the slope (the rate of change of \(y\) for a unit change in \(x\)). This is the standard equation used in simple linear regression.

Step 3: Detailed Explanation:
Since the given equation has \(x\) raised only to the first power, with no \(x^2\) or higher terms, and no \(x\) in a denominator, plotting \(y\) against \(x\) produces a straight line with slope \(b\) and intercept \(a\).
A parabola would need a squared term such as \(y = a + bx^2\), which is not present here.
A hyperbola would need an inverse or product relationship such as \(xy = c\), which is not the case here.
A sigmoid curve is an S shaped curve that arises from equations involving exponential terms, unlike this simple linear form.

Step 4: Final Answer:
The equation \(y = a + bx\) is the equation of a straight line.
\[ \boxed{\text{Straight line}} \]