# any general method

• Aug 6th 2009, 12:22 AM
bluffmaster.roy.007
any general method
In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?
• Aug 6th 2009, 12:42 AM
Mush
Quote:

Originally Posted by bluffmaster.roy.007
In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?

It's a straight line, therefore it has an equation of the form:

$y = mx+c$

Where m is the gradient and c is the y-intercept.

To find m, use the following:

$m = \frac{y_2 - y_1}{x_2-x_1}$

Using the coordinates that have no unknowns.

Then find the y intercept by plugging one of the coordinates into your new equation and solve for c.

One you've done that, put the points (x,3) into the equation and solve for x.
• Aug 6th 2009, 01:21 AM
bluffmaster.roy.007
not able to solve can u show me how to since slope of

the first two cordinates is zero so can the value of x be 5 ....what is the value of x
• Aug 6th 2009, 01:39 AM
Mush
Quote:

Originally Posted by bluffmaster.roy.007
not able to solve can u show me how to since slope of

the first two cordinates is zero so can the value of x be 5 ....what is the value of x

The slope is not zero. You have two coordinates (5,3) and (3,2).

Therefore, the gradient is calculated as follows:

$m = \frac{3-2}{5-3} = \frac{1}{2}$

So you know that the equation is:

$y = \frac{1}{2}x + C$.

Now you have to find C. Do this by taking one of the coordinates (either (5,3) or (3,2)) and plugging it into the equation, and solve for C.

$3 = \frac{1}{2} (5) + C$

$\therefore C = 3 - \frac{5}{2} = \frac{1}{2}$

So you're equation is $y = \frac{1}{2}x + \frac{1}{2}$

Now, plug in the coordinate (x,3) and solve for x.
• Aug 6th 2009, 05:34 AM
mr fantastic
Quote:

Originally Posted by bluffmaster.roy.007
In a coordinate system, if three points (5, 3), (x, 3) and (3, 2) lie on a same line, then find a value of x?

If you plot (5, 3) and (3,2) and run a line through them it is clear that if (x, 3) lies on this line then x = 5.