Question 226311
Wath is the slope of the line passing through (-5,5) and (9,-9)


Step 1.  We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).


Step 2.  The slope of the line m is given as


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


where for our example is x1=-5, y1=5, x2=9 and y2=-9 (think of {{{slope=rise/run}}}).  You can choose the points the other way around but be consistent with the x and y coordinates.  You will get the same result.


Step 3.  Substituting the above values in the slope equation gives


{{{m=(-9-5)/(9-(-5))}}}


{{{m=-14/14=-1}}}


Step 4.  The slope is calculated as {{{-1}}} or {{{m=-1}}}


Step 5.  Now use the slope equation of Step 2 and choose one of the given points.  I'll choose point (-5,5).   Letting y=y2 and x=x2 and substituting {{{m=-1}}} in the slope equation given as,


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



{{{ -1=(y-5)/(x-(-5))}}}


{{{-1=(y-5)/(x+5)}}}


Step 6.  Multiply both sides of equation by x+5 to get rid of denomination found on the right side of the equation



{{{-(x+5)=(x+5)(y-5)/(x+5)}}}



{{{ -(x+5)=y-5}}}



Step 7.  Now simplify and put the above equation into slope-intercept form.


{{{-x-5=y-5}}}


Add 5 from both sides of the equation


{{{-x-5+5=y-5+5}}}


{{{-x=y}}}


{{{y=-x}}}   This is in slope-intercept form where the slope m=-1 and y-intercept b=0


Step 8.  See if the other point (9,-9) or x=9 and y=-9 satisfies this equation


{{{y=-x}}}


{{{-9=-9}}} which is true


 So the point (9,-9) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.


Step 9.  ANSWER:  The equation of the line is {{{y=-x}}}


Note:  above equation can be also be transform into standard form as


{{{x+y=0}}}


See graph below to check the above steps.


*[invoke describe_linear_equation 1, 1, 0]


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J