Question 431238
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which equation represents a line that passes through the points (2,3) and (-1,-3) ?
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        The solution in the post by @mananth is incorrect:  it has many arithmetic errors.

        I came to bring a correct solution.



<pre>
Having two points given by their coordinates, we first calculate the slope of the line.


To calculate the slope  m, use the formula  m = {{{(y2-y1)/(x2-x1)}}}.

The numerator   is  y2 - y1 = -3 - 3 = -6.

The denominator is  x2 - x1 = -1 - 2 = -3.


So, the slope is  m = {{{(-6)/(-3)}}} = 2.

							
We look for equation in the form 

    y = mx + b	= 2x + b.


We just know the slope 'm';  so, we only need to find 'b'.


To find 'b', plug coordinates (2,3) in this equation

    3 = 2*2 + b

and find  b = 3 - 4 = -1.

		 
So the equation  of the line is  y = 2x - 1.    <<<---===  <U>ANSWER</U>


At the end, to be sure, we must check that this equation satisfies coordinates of both points.
I leave this check to you, since it is pure mechanical job.
</pre>

Solved.