Graph 3x + y ≤ 5?

Question

REALLY LOST

Answer 1

Okay, you have a linear equation with an inequality. This is going to identify a line, plus everything in the x-y plane that is on ONE side of the line.

(1) First, treat it as an equality. Start by graphing the line 3x + y = 5. (If they're asking you to graph inequalities, I assume you've already covered that, but I'll go through the steps anyway.)

Let's pick a couple of points on 3x + y = 5.

When x=0:

3x + y = 5
3*0 + y = 5
y = 5

So, (0,5) is one of the points.

When x=2:

3x + y = 5
3*2 + y = 5
y = 5 - 6
y = -1

So, (2,-1) is another.

Plot those two points on a graph, and with a ruler connect them in a straight line. This gives you the solutions to 3x + y = 5.

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Now, since you had "≤ 5" instead, the solution is not only those values for x and y where 3x+y=5, but ALSO all the values for x and y where 3x+y adds up to a number smaller than 5. That will be all the area on ONE side of the line.

So, your next step is...

(2) Shade one side of the line, to identify the portion of the plane which is also part of the solution.

Which side, though? If you are lost, just try out a couple of points. Choose a point that's on one side of the line. For example (0,0) is an easy one, that's sort of below-left of the line. Does that satisfy the inequality?

3x + y ≤ 5
3*0 + 0 ≤ 5
0 ≤ 5

Yes, it does. So, whichever side of the line the origin (0,0) falls on, everything on that side of the line is part of the solution.

Just for fun, pick a point that's on the other side (above-right) of the line, such as (3,3). Does that satisfy the inequality?

3x + y ≤ 5
3*3 + 3 ≤ 5
12 ≤ 5

No, it doesn't. So the parts of the plane that are on the same side of the line as (3,3) are NOT part of the solution.

Your solution will have a solid line (indicating that the points on the line are part of the solution) and a shaded portion of the plane (indicating that the shaded areas are part of the solution). The shading should go from the line to the edges of the graph that you drew, on one side of the line only.

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One final note:

If the equation had been "<" instead of "≤", the convention is that you should draw 3x+y=5 as a DASHED line to indicate that it is NOT part of the solution.

When you're going through the "graph the equality" part, keep in mind whether the equality is part of the solution set, and draw either a solid (it is included) or a dashed (it is not included) line as appropriate.

Answer 2

Put it into 'y=mx+b' format

So y≤-3x+5

Plot 5 as the y-intercept (on the graph, put a dot on the y-axis on the fifth line up).

3 is the slope, or better read as 3 over 1. From point 5, go three spaces up, and one space over (rise over run!). Plot the point where you finish moving and repeat the step until you make a straight line.

The line is a solid line, if it was less than (wihout the line under the sign) then it would be dotted.

Shading the solution is also really simple. Choose a point (such as 0,0). Put the two 0's in for x and y into the formula respectively. If 0≤3(0)+5 works out, which it does, then shade from your line towards the point 0,0

Answer 3

make a line with an arrow pointing to the left side [since the x is on the left side of the equation] then put 6 lines. write down the numbers for each line like the first line would be zero then the second would be 1. continue until you get to 5. make sure the lines are on the positive side. then put an open circle on the 5 line and darken the line all the way from the arrow to the open circle to show it going left until 5. hope this helps!
<===|=|=|=|=|=(|)----
------ 0 1 2 3 4 5-------

Answer 4

I know this may be a little costly, but look into buying a TI-83 Plus.