Graph two more functions in the same family for witch the parameter being changed is the y-intercept, b

As both the equation have same slope i.e m , so lines will be parallel, but their Y - intercept are different i.e distance from the origin where it cuts the y-axis are different i.e at a distance of p and q from origin.

MrRoyal MrRoyal · Answer 2 · 2021-10-28T20:33:04+02:00

The y-intercept of a function is the point where the graph, crosses the y-axis.

See attachment for the graphs of [tex]\mathbf{y = 2x + 3}[/tex], [tex]\mathbf{y = 2x + 5}[/tex] and [tex]\mathbf{y = 2x - 3}[/tex]

The function is given as:

[tex]\mathbf{y = mx + b}[/tex]

The above function is an illustration of a linear function, where:

m represents slope
b represents the y-intercept

Assume that:

[tex]\mathbf{m = 2, b= 3}[/tex]

The function becomes

[tex]\mathbf{y = 2x + 3}[/tex]

If the y-intercept is changed to other values, the function can take any of the following forms:

[tex]\mathbf{y = 2x + 5}[/tex]

[tex]\mathbf{y = 2x - 3}[/tex]

See attachment for the graphs of [tex]\mathbf{y = 2x + 3}[/tex], [tex]\mathbf{y = 2x + 5}[/tex] and [tex]\mathbf{y = 2x - 3}[/tex]