what is an equation for a line indicating these points (4,1/2) and (0,5/2)?

Question

y=mx+b

Answer 1

you've indicated slope-intercept form, where y is the y intercept. that's given as 5/2 by the point (0,5/2).

now you just need the slope, m.

m = (5/2 - 1/2)/(0 - 4) = -1/2.

thus y = -x/2 + 5/2.

steve b has got the slope backwards, it's dy/dx, not dx/dy.

Answer 2

Basic equation for a line is y = m*x + b.
The line has to land on both these points so the following statemnts must be true:

1/2 = 4m + b
5/2 = 0m + b

Based on the 2nd equation, b = 5/2
Plug that into the first equation and you find that

1/2 = 4m + 5/2
=> -4/2 = 4m
=> -1/2 = m

y = -1/2 * x + 5/2

Answer 3

m = (y2-y1)/(x2-x1)
= (5/2-1/2)/(0-4)
= 2/-4 = -1/2

y=mx+b
5/2=-1/2*0 + b
5/2 = b

Therefore, your equation is y=-1/2x+5/2

Check your work (something the previous posters forgot to do!):
y=-1/2 * 4 + 5/2
=-4/2 + 5/2 = 1/2

Answer 4

y = -2x + 5/2