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A straight line has equation y=3/2x + 6 write down the coordinates of a point that lies...

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tafflaff | eNotes Newbie

Posted May 26, 2013 at 10:05 PM via web

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A straight line has equation y=3/2x + 6

write down the coordinates of a point that lies on the line and find the x intercept of the line

 

 

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ishpiro | Teacher | (Level 1) Associate Educator

Posted May 27, 2013 at 12:42 AM (Answer #1)

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The coordinates of ANY point that lies on the line?

If x-coordinate of a point on the line is x = 2, then y-coordinate has to be

`y = 3/2 * 2 + 6 = 3+6=9`

(2, 9) is a point on the line

x-intercept is the poipnt where the line intersects the x-axis. This means the y-coordinate of this point is y = 0. The x-coordinate can be found by plugging in y =0 into the equation of the line:

`0 = 3/2 x + 6`

`-6=3/2 x`

`x=-12/3 = -4`

The x-intercept of this point is (-4,0).

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jose26425 | High School Teacher | (Level 1) Adjunct Educator

Posted May 30, 2013 at 2:22 AM (Answer #2)

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To find the coordinates of a point on the line, all you have to do is pick a value for "x" and plug it into the equation, the resulting number will be the "y' in your coordinate.

The Steps:

1) Choose a value for x. Let's try 0. Plug in for x and solve for y.

    y = 3/2x + 6

    y = 3/2(0) + 6

    y = 0 + 6

    y = 6

2) One of the points on the line is (0,6). You can do this with any value for x. I just chose "0" because it was the nicest and easiest to plug in. 

 

To find the x-intercept: 

Remember that the x-intercept is the point where the line cross the x-axis. If you remember you graphing, the "y" of the coordinate will always be 0.  So plugging a "0" in for y and solving for x will give me the x-intercept.

The Steps:

1) Plug in a "0" for y. Solve for x. 

    y = 3/2x + 6

    0 = 3/2x + 6

    -6            -6

_______________

    -6 = 3/2x

   *With a calculator, type in -6 / (3/2)**

     x = -4. 

 

The x-intercept is (-4,0). 

 

Hope this helps! Good luck!

 

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