Question 78033
Hello.. here goes the solution.


find the slpoe of the line that passes through the points (-4,1)and (3,8).


The slope of the line passing thru 2 points (x1, y1) and (x2, y2) is given by: 


{{{m = (y1 - y2)/(x1 - x2)}}} 


Substituting for the points from the given data, we get: 


{{{ m = (8 - 1)/(3 - (-4)) }}} 


{{{ m = (7/ 7) }}} 


 m = 1 


This represents the slope of the line. 


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find the equation in slope-intercept form , of the line that passes through the points (-5,2)and (-4,1)


The equation of the line in the slope intercept form is given by:


{{{ y - y1 = m(x - x1)}}} ------------(1)


Where m is the slope, which is given by:  {{{m = (y1 - y2)/(x1 - x2)}}}  


substituting the co-ordinates in the slope, we get: 


{{{ m =  (1 - 2)/(-4 -(-5)) }}} 



{{{ m = -1/1}}} 


==> m = -1 


Now substitute the slope and the one of the co-ordinate in Equation (1). We get:


y - 2 = (-1)(x - (-5))


y - 2 = (-1)(x + 5) 



y - 2 = - x - 5 


y - 2 + x + 5 = 0 


y + x + 3 = 0 


represents the equation of the line in the slope intercept form.



hence, the solution.