Graph 2x+4y<1, show steps please??!!?

Answer 1

x-intercept: Set y = 0 and solve for x
2x + 4(0) = 1
2x = 1
x = 1/2
Put a dot at (1/2,0)
y-intercept: Set x = 0 and solve for y.
2(0) + 4y = 1
4y = 1
y = 1/4
Put a dot at (0,1/4)
Now connect the two points with a straight dotted line.
You need a test point to see which side to shade.
Pick any point that is not on the line. (0,0) is not on the line
2(0) + 4(0) < 1
0 + 0 < 1
0 < 1 This is true so shade the side that contains that point.

Answer 2

First find the line 2x+4y=1

Find the intercepts is the easiest way since it doesnt go through (0,0)

x intercept 2x+4(0)=1 => x = 1/2
y intercept 2(0)+4y=1 => y = 1/4

Connect these with a DASHED line. Why? Because the inequality did not include the equality case so the line is not in your area.

Step 2 - Find a test point. We already know (0,0) is not a point on the line so we can check it.

2(0)+4(0)=0<1 So (0,0) is in our region.

Step 3 - Shade in the side of the dashed line that contains (0,0)

and your done

Answer 3

2x + 4y < 1
4y < -2x + 1
y < (-1/2)x + (1/4)

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