The formula y = b – 4x describes a family of parallel line graphs. What is the equation of the member of this family that has an x-intercept

All right, so we know the line intercepts the x-axis when x = 1/2. When a line intercepts the x-axis, y = 0 (because that's where the x-axis is). Therefore fill in x = 1/2 and y = 0 in your equation.

This gives

0 = b - 4*1/2

add 4*1/2 to both sides

4*1/2 = b

multiply 4*1/2 and flip the equation

b = 2

Fill this in in the equation

y = b-4x

and you'll find

y = 2-4x

Thankyou for your time, I am currently struggling as it is a late night and you have legitimately managed to refresh my mind! Kudos. 

You're welcome,

or

'graag gedaan' as they say in Dutch