Question 750316: show that the points (a,0),(0,b) and 3a,-2b) lie on a straight line. find its equation
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Two points determine a line.
We can calculate the slope of the line between 2 of those points.
From the slope and the coordinates of one of the points, we can get the equation of the line. If the coordinates of the third point satisfy that equation, the third point lies on that same line.
The slope of the line connecting (a,0) to (0,b) is
Since the y-intercept is at (0,b), b is the intercept, and we can write
 as the slope-intercept form of the equation of the line connecting (a,0) to (0,b).
Substituting the x-coordinate of (3a,-2b) into the equation we can find if that point lies on the same line.
For  , the point on the line has
 so point (3a,-2b) lies on the same line as the other two points.
If we were not asked for the equation of the line, we could calculate the slopes for two different pairs of points. If we found the same slopes connecting two of the points with the other point, that would mean they all lie on the same line.
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