Question

Which graph correctly represents x + 2y ≤ 4?

Answer 1

X + 2y < = 4
2y < = -x + 4
y < = -1/2x + 2

u will have a solid line (because there is an = sign in the problem)....the slope will be -1/2...so ur line is going down....u have a y int (where ur line crosses the y axis at (0,2).....u have an x int (where ur line crosses the x axis at (0,4)..ur line will be shaded below the line.

Answer 2

Step-by-step explanation:

$x + 2y \leq 4$

To graph this inequality we replace <= symbol with = sign

$x + 2y =4$

subtract x on both sides

$2y =-x+4$

divide both sides by 2

$y= \frac{-1}{2} x +2$

Graph the equation using a table

LEts assume some number for x  and find out y

x                           $y= \frac{-1}{2} x +2$

-2                           3

0                             2

2                             1

Now graph the equation using points (-2,3)  (0,2)(2,1)

use solid line for graphing

Now use test point (0,0) for shading

$x + 2y \leq 4$

$0 + 2(0) \leq 4$

$0 \leq 4$     true

So  we shade the region that contains (0,0)

the graph is attached below