Question
What do you understand by ‘parametric shift of a line’? How does a line shift when its: (i) slope decreases, and (ii) its intercept increases?

Answer

Considering the equation of a straight line as:

$\text{b}=\text{ma}+\in$

Where m = slope of straight line, m > 0

$\in$ = intercept on vertical axis, $\in$ > 0

Also, when a increases by 1 unit, the value of b increases by m units.

The parameters ε and m are parameters of a graph.

As the value of m increases, the straight line rotates upward around the same vertical intercept. This movement is an example of parametric shift of the graph.

  1. A straight line rotates downward around the same vertical intercept as its slope decreases.
  2. A straight line shifts parallelly upward when its intercept increases.

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