Would really be appreciated with this one!

create two ordered pairs (for example) (7,82) and (4, 18)
write an equation of a line that goes through these two points using each method.
point-slope form
slope-intercept form

Point slope is nicer
y-y1=m(x-x1)
goes through the point (x1,y1) and has a slope of m

slope itnercept
y=mx+b
m=slope
b=y intercept

first find slope
slope between 2 points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
given
(7,82) and (4,18)
slope=(18-82)/(4-7)=-64/-3=64/3

point slope
point is (7,82) or you can do (4,18)
I'll do both
y-82=(64/3)(x-7) or
y-18=(64/3)(x-4)
those both work

slope intercept
slope is 64/3
y=64/3x+b
find b
input a point
(4,18)
18=64/3(4)+b
18=256/3+b
minus 256/3 from both sides
note: 18=54/3
-202/3=b
y=64/3x-202/3 is equation in slpe intercept