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:
$\displaystyle y = mx+c$
Where m is the gradient and c is the y-intercept.
To find m, use the following:
$\displaystyle 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.
The slope is not zero. You have two coordinates (5,3) and (3,2).
Therefore, the gradient is calculated as follows:
$\displaystyle m = \frac{3-2}{5-3} = \frac{1}{2} $
So you know that the equation is:
$\displaystyle 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.
$\displaystyle 3 = \frac{1}{2} (5) + C $
$\displaystyle \therefore C = 3 - \frac{5}{2} = \frac{1}{2}$
So you're equation is $\displaystyle y = \frac{1}{2}x + \frac{1}{2} $
Now, plug in the coordinate (x,3) and solve for x.