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?

Considering the equation of a straight line as

b = ma + ε

Where m = slope of straight line, m > 0

ε = intercept on vertical axis, ε> 0

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

The parameters εand 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.

(i) A straight line rotates downward around the same vertical intercept as its slope decreases.

(ii) A straight line shifts parallelly upward when its intercept increases.