Find f(g(g(x))) if f(x)= (ax+b)/(cx+d) and g(x)=mx

Hello from MrBillDoesMath!

  x = 4, slope intercept form is y = 2x + 11

Discussion:

A vertical line  goes straight up and down. The only thing "fixed" about it is its x value. Hence a vertical line has an equation like "x = ?". As your line passes through (4, -3), with x value 4. its equation is x = 4.

The slope intercept form of a line is " y = mx + b" where m is the slope of the line and b is its y intercept. We are told the desired line is parallel to  y = 2x -1 which  means both lines have the same slope (which is 2, boldfaced, above). So,  we know the slope intercept form is

y = 2x + b

but we are also told the line passes through (-3,5). Substituting these values in the above equation gives

y = 2x + b

5 = 2 (-3) + b

5 = -6 + b

b = 5 + 6 = 11

The final slope intercept form is y = 2x + 11

Regards, MrB