Erika was absent from class the day her teacher taught how to graph a line. Erika text you the next day asking for your help. Explain to Erika how to graph the line 3y+x=21. Use complete sentences!

Answer 1

Main thing to keep in mind is that this is an equation for a straight line. So, all you need is two points and then draw a line through them.

Since a straight line contains many it's reasonable to ask which two points. Recall that each point has an x coordinate and a y coordinate. So, you have to come up with two coordinates for one point and two for the other. So how do you do this? Easy. Pick values and plug them into the equation to get the other coordinate value. Here's how:

Pick y = 0 and plug in to get x = 21. So first point is (21,0)

Pick x = 0 and get 3y= 21. Now divides both sides by 3 to get y = 7. So second point is (0,7)

Now all you have to do is plot the points on a graph and draw a straight line through them.

Note that you could pick any values for x and y what you want. We picked 0 as shown above to make things easy. We could have picked any other values we pleased. Be aware though that using zero can be a no-no if plugging it it results in dividing by zero. Not so in this case so it's okay.

Answer 2

METHOD 1: Two points determine a line.

 For the formula 3y + x = 21:

      When x=0, y=7     That’s the point (0,7)

      When y=0, x=21   That’s the point (21,0)

  Connect the dots; then extend the line in both directions.

METHOD 2: Use a point and the slope of the line (convert to slope-intercept format)

    In slope-intercept format, the equation is y = (-1/3)x + 7      ; this is y=mx+b

              The slope m= -1/3    the y-intercept is the point (0,7)

    Plot the point (0,7); then for each additional three x values subtract one y value.

               This is “rise over run” where rise is negative when run is positive.

               If you move right to the point where x=21, then you must move down to y=0.

                                                                 [That is, 7 – 21/3]

Answer 3

first re write the equation in standard form

3y+x=21

3y = -x +21

y = -1/3x +7

so our slope is -1/3 and our y intercept is 7

go to (0,7) - the y intercept and put a point.

Then we use rise over run to plot the slop from our intercept point.

so from (0,7) go down one and right three, then do that one more time.

Now go back to (0,7) and go up on and left three, repeat that one more time.

Now connect the dots.

Answer 4

I won't be using complete sentences because you should use your own voice for such, but what I can do is help walk you through the process so you can write your own.

Start by Isolating y. Start by subtracting x:

3y + x - x = 21 - x

3y = -x + 21

Divide by 3:

3y / 3= (-x + 21) / 3

y = -^x/₃ + 7

We now have a slope-intercept format. Place some values into x and find y. Suggest using numbers that are divisible by 3:

x| 0 | 3 | 6 | -3| -6|

y| 7 | 6 | 5 | 8 | 9 |

Place points onto a graph and connect the dots:

^

| y

|

|

<---------------------+----------------------->

| x

|

|

V