Question

For specifying a straight line how many geometrical parameters should be known?
A. 1
B. 2
C. 4
D. 3

Answer 1

Hint: Parameter is a constant that influences a function or output or the behaviors of an equation. We will find the parameter of an equation of a line. There are various forms of the equation of a line. We will find the parameters of the equation of a line.

Formula Used:
Form of equation of line:
Slope intercept form: $y = mx + c$
Point slope form: $y - {y_1} = m\left( {x - {x_1}} \right)$
Standard form: $ax + by = c$
Intercept form: $\dfrac{x}{a} + \dfrac{y}{b} = 1$

Complete step by step solution:
Slope intercept form:
$y = mx + c$, where $m$ is the slope and $c$ is $y$ intercepts.
Here $y$ and $x$ are variables.
The parameters are $m$ and $c$.
The parameters for $y = mx + c$ is 2.
Point slope form:
$y - {y_1} = m\left( {x - {x_1}} \right)$, where $m$ is the slope and $\left( {{x_1},{y_1}} \right)$ is the point on the line.
Here $y$ and $x$ are variables.
The parameters are $m$ and $\left( {{x_1},{y_1}} \right)$.
The parameters for $y - {y_1} = m\left( {x - {x_1}} \right)$ is 2.
Standard form:
$ax + by = c$, where $a$, $b$, and $c$ are constant.
The parameters are $a$, $b$, and $c$.
The parameters for $ax + by = c$ is 3.
Intercept form:
$\dfrac{x}{a} + \dfrac{y}{b} = 1$, where $a$ is $x - $intercepts and $b$ is $y$ intercepts.
The parameters are $a$ and $b$.
The parameters for $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is 2.
So, the number of geometrical parameters for specifying a straight line should be known is 2.

Option ‘B’ is correct

Note: Do not use the standard form equation of a line to find the parameters. As $a$, $b$, and $c$ are not geometrical parameters. We need only 2 geometrical parameters to find the equation of the line for specifying a straight line.