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9x - 2y = 11
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High School Teacher
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:
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.
Posted by neela on June 16, 2009 at 10:55 AM (Answer #1)
Middle School Teacher
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
-2y = 11 - 9x
divide through by -2
y = -5.5 + 4.5x
Rearrange to put x first, and change to fractions.
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.
Posted by sbinkowski on June 18, 2009 at 4:23 AM (Answer #2)
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