How would you graph -x+2y=6?

Question

Need help with graphing this problem.

Answer 1

Hi Monique,

 

  The simplest way might be to let let x=0 and solve for y, which yields y=3.  You now know that the point (0,3) will be a point on your graph.  (It is also the y-intercept, where the graph crosses (intercepts) the y-axis.

 

  Now let y=0 and solve for x, which yields x=-6.  Therefore the point (-6,0) also is a point on the graph (and is the x-intercept where the graph crosses the x-axis).

 

Plot each point on a piece of graph paper (or computer screen).  The original equation in a linear one, it plots as a straight line, and you only need two points to uniquely define a line.  Now draw a straight line through these two points.  You are home free.

Answer 2

Monique,  Sometimes, your teacher wants more than just the graph !   The prior solutions were ALL very good.  As a former teacher, I would want my students to understand the Algebra behind  "Y = MX + B " more than just plotting the intercepts.  Yes, that does work!  But suppose the graphing medium is insufficient to find "rational points" or just not reliable to determine other significant positions in the quadrants. Then, the student NEEDS to know the formula and its applications.   -X + 2Y = 6  invokes the need to use transformations, so that the slope can be determined.  This is the most significant aspect of graphing linear equations and every student will need to know this for future Mathematics.

1)  Isolate the Y-term ( 2Y )  by adding X  to both sides:    2Y =  X  +  6   will be the next line.  2)   Divide by that coefficient "2" to get  Y  alone.  That will provide you with  " MX + B "  on the other side !   Y = 1/2 X +  3  is the last step.  The most common error for students here is getting the three instead of six.  They forget to divide BOTH terms by the two !  3) Identify the slope and Y-intercepts :   M = 1/2   while  B = 3 ( which is the ordered pair (  0, 3 ).  Now, Monique, this is where it gets interesting... Slope is the pattern that every point has with reference to its preceding points...which provides the "angle" of inclination or depression.....sort of like a ramp that a car can drive up or down upon.  Think of all the possibile applications that this might suggest.  Let's go to the graph of this line:  Take ANY point that lies on this line.  We know that  ( 0 , 3 ) is on the line.  That was the intercept we found earlier. Now the slope takes you to the next point on that same line !!!  The "slope movement" is  UP one unit and RIGHT two units from that first point.  You get the point ( 2 , 4 ).  Go ahead and test this.  Repeat for the next point.....

( 4 , 5 ).  And the next point  ( ( 6 , 7 ).   Check each set into your equation.... Are they correct ?  THAT is what slope does !  There is one more thing I can show you :  Slope can have a second set of movements, since the line can travel two opposite directions  Here, the M =   -1/-2   which still gives you the same slope but different direction.  Now, the slope movement is " DOWN 1   and  LEFT 2 ":  Heh, let's go back to  ( 0 , 3)  and try it the other way.   Go down one  and left two to find the next point below...... ( -2 , 2 )   Go ahead and try this yourself. The point after that... (  - 4, 1 ).  Now, you have five points, all which "satisfy" the equation  -X + 2Y = 6 , so they are all part of the solution set that makes up the equation itself.  Good luck to you, and if you have any other questions, please free to contact our WyzAnt.com or me or both ! 

 

Charles S.

Hendersonville, NC   

Answer 3

-x + 2y = 6

 

find a value for x and plug in to above to get value of y. Let's try x = 0, so:

 

0 + 2y = 6

 

y = 3, so we have one point (0, 3). Graph this on graph paper. Now, let's pick x = 1, so:

 

 

-1 + 2y = 6

 

2y = 7

 

y =7/2

 

now, we have another point (1, 7/2). Graph this also. Now, just connect both points using a ruler. At both ends of the line drawn, draw an arrow (eg.       <----------->)