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9x - 2y = 11

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bulldog13 | Student, Grade 9 | eNotes Newbie

Posted June 16, 2009 at 7:57 AM via web

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9x - 2y = 11

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neela | High School Teacher | Valedictorian

Posted June 16, 2009 at 10:55 AM (Answer #1)

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9x-2y=11.

This is a linear equation involving two varibles x and y.

It represents a straight line , if we plot the values of x and y.

To find the y value for any given x value, we change the equation  by adding equal quantity or dividing the same number both sides:

9x-2y+2Y-11=11+2y-11 or

2y=9x-11 . Divide both sides by 2 to get,

y=(1/2)(9x-11).Now,giving various values to x we get the corresponding values of y satisfying the equation:

x         values:      0 1     2       3       4        5

y=(1/2)(9x-11):  -5.5 -1    3.5     8     12.5     17

If we plot the above values,we observe  that this equation represents a straight line and the pair of coordinates of any point on this line (or the line extended both sides )represents many solutions of the given equation.

The line has a slope of 9/2,which means for every unit  increment in x, there is an increment of  4.5 in y.

Intercepts: Put y=0 in the equation:9x- 2*0=-11.Then 9x=-11. So, x=-11/9. |||rly when x=0 , y=-5.5. The line 9x-2y=11, inercepts the lx axis at = -11/9 and the y axis at -5.5.

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sbinkowski | Middle School Teacher | (Level 1) Adjunct Educator

Posted June 18, 2009 at 4:23 AM (Answer #2)

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What exactly would you like to do with 9x - 2y =11?

You can graph it. That's what I assume you would like to do with it. In order to graph the equation, you can set up a T-chart or you can find the x and y intercepts, or you can solve for y and use the y-intercept and slope.

I am going to solve for y and use the y-intercept and slope. Keep in mind that no matter which way you choose, you should always get the same line graphed.

You want to get y all by itself on the left side of the equation.

9x - 2y = 11

-9x         -9x

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-2y = 11 - 9x

divide through by -2

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y = -5.5 + 4.5x

Rearrange to put x first, and change to fractions.

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y = (9/2)x - 5_1/2

The number in front of x will be your slope (rise over run). The number out by itself (the constant) is your y-intercept. The first thing is to plot the y-intercept, -5_1/2. Start at the origin, (0,0). Go down to -5_1/2 on the y-axis. That will be your first point. From that point, you will mark 2 more using your slope. You need to go up 9 from your y-intercept and then to the right 2. Make a mark there. From that new point, go up 9 and to the right 2 again. You should have made 3 points that form a line. If not, go back and count again. Sometimes it is easy to mess things up there.

Remember that you start at the y-intercept! Start there and use your slope to make 2 more points.

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