The Loyalists remain

[Exotic]

can someone help me with my homework how do i find the intersection between something like f(x)=2x-4 and a line that crosses over the points a a=(-1, 5) and b=(1, 9)

so you need to find the gradient of the second line first, you already have the points a and b so first do:

m=(y2-y1)/(x2-x1) = (9-5)/(1--1) = 4/2 = 2

so now that you have the gradient, use the equation y-b=m(x-a) and plot either a or b into the equation:

y-b=m(x-a)
y-5=2(x--1)
y-5=2x+2
y=2x+7

now that you have the second equation, to find the intersection make both the equations equal to each other and find x:

2x+7=2x-4
2x=2x-11
x=0

since x=0, you have shown that these lines don't intersect and you can plot a graph as well for y=2x+7 vs y=2x-4 to prove it. they also won't intersect because they both have the same gradient.

can't remember if this is the way you do it but i think it is