Question

How do i solve and graph y \geq 5" align="absmiddle" class="latex-formula">

Answer 1

One way is to make it into slope intercept form which is
y=mx+b
m=slope
b=y intercept or where the line will go though the y axis
treat the equal to or greater than sign as equals for now

5x-y=5
subtract y from both sides
5x=5+y
subtract 5
5x-5=y
put the sign back in
5x-5 ≥ y
reverse
y ≤ 5x-5

one way is to subsitute values and get values out so
if x=1 then
y≤5(1)-5
y≤0
(x,y)
(1,0)
(2,5)
(3,10)
(4,15)
(0,-5)

plot the points
then the ≤ sign
since ther is an underline, that means that the points are included so draw a solid line through the points

then figure out which side to shade on
the easy way is, is the point (0,0) a solution?
subsitute
0 ≤ 5(0)-5
0 ≤ -5
false so we shade the section that does not include the point (0,0) in it
the graph would look like this attachment

Answer 2

    (you have to put y alone {Ex: y = 12x + 3 (yis alone on one side)}



5x - y ≥ 5       (subract 5x from each side)
-y ≥ -5x + 5   (divide - or -1 from each side)  Note: when you are dividing or multiplying anything negative the sign changes
y ≤ 5x - 5 <--- answer


As for graphing you take the equation and graph it normally, but with a slight change. since y is less than or equal to 5x - 5, you have to color on the spACE BELOW the graphed line.

see picture: