Question

choose two points for a straight line so that the slope becomes -0.25.

this is all i'm given but i don't understand what it means. Do I pick two points and make a formula? wouldnt the slope be 0.25x + 1 lets say and you can get points by plugging in x?

Answer 1

Yes : )
You know that -0.25 means your line is slanting downwards when looked at from the left most point to the right most point.
And you also know that 0.25 as a fraction is 1/4
so your slope from the first point to the next point is ... down one unit, and move to the right 4 units... and plot a second point : )

Answer 2

just work backwards
slope = -.25 = -1/4

slope = change in y/change in x
so all you need is a pair of numbers with a difference of -1
and another pair with a difference of 4

for the first one, how about 5 - 6 <----- those are y's
for the 2nd , how about 7-3 <---- those are x's

so (3,6) and (7,5) would do.

Of course there would be an infinite number of such combinations

<b>OR</b>

you could just take any equation of the form y = (-1/4)x + b
put in anything you want for b, how about

y = (-1/4)x + 5

now pick any x, preferably a multiple of 4 to avoid fraction, and get the y
e.g. let x = 8, then y = (-1/4)(8) + 5 = 3 ----> point (8,3)
let x = -4, then y = (-1/4)(-4) + 5 = 6 ----> point (-4,6)
check: slope = (3-6)/(8+4) = -3/12 = -1/4