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: Look at the form of the equation.
The relation given is $y=a+bx$, where $y$ stands for height and $x$ for age.

Step 2: Identify what kind of equation this is.
Here $x$ appears only to the first power, with a constant $a$ added to a constant $b$ times $x$. This is the exact form of a simple linear equation, the same one used in linear regression, where $a$ is the intercept and $b$ is the slope.

Step 3: Compare with the other shapes listed.
A parabola would need an $x^2$ term, a hyperbola would need $x$ and $y$ multiplied together or $x$ in a denominator, and a sigmoid curve would need an exponential term. None of these features appear in $y=a+bx$.

Step 4: Conclude.
A plot of $y$ against $x$ for this equation gives a straight line with slope $b$.
\[ \boxed{\text{Straight line}} \]