How do you write the equation of a line in point slope form and slope intercept form given points (-1, -5) (-7, -6)?

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Answer 1 · 2018-03-20T11:35:56

The equation of the line in slope intercept form is #y= 1/6x-29/6.#
The equation of line in point slope form is #y+5=1/6(x+1) #

The slope of the line passing through

#(-1,-5) and (-7,-6)# is

#m= (y_2-y_1)/(x_2-x_1)= (-6+5)/(-7+1)= (-1)/-6=1/6#

Let the equation of the line in slope intercept form be

#y=mx+c or y=1/6*x+c#. The point #(-1,-5)# will satisfy

the equation .So, # -5= 1/6*(-1)+c # or

#c= -5+1/6=(-29)/6#. Hence the equation of the line in

slope intercept form is #y= 1/6x-29/6.#

The equation of line in point slope form passing through

#(x_1,y_1)# having slope of #m# is #y-y_1=m(x-x_1)#.

The equation of line passing through #(-1,-5)# having slope of

#1/6# is #y+5=1/6(x+1) # [Ans]