Question 223788
Please help me graph the line containing the given pair of points & find the slope (2,0), (-3,-2)


Step 1.  The slope of the line m is given as


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


where for our example is x1=2, y1=0, x2=-3 and y2=-2 (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 2.  Substituting the above values in the slope equation gives


{{{m=(-2-0)/(-3-2)}}}


{{{m=-2/-5}}}


{{{m=2/5}}}


Step 3.  The slope is calculated as 2/5 or {{{m=2/5}}}


Step 4.  Now use the slope equation of step 1 and choose one of the given points.  I'll choose point (-3,-2).   Letting y=y2 and x=x2 and substituting m=-3 in the slope equation given as,


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



{{{ 2/5=(y-(-2))/(x-(-3))}}}


{{{ 2/5=(y+2)/(x+3)}}}


Step 5.  Multiply both sides of equation by (x+3) to get rid of denomination found on the right side of the equation



{{{ 2(x+3)/5=(x+3)(y+2)/(x+3)}}}



{{{ 2(x+3)/5=y+2}}}



Step 6.  Now simplify and put the above equation into slope-intercept form.


{{{2x/5+6/5=y+2}}}


Subtract 2 from both sides of the equation


{{{2x/5+6/5-2=y+2-2}}}


{{{2x/5-4/5=y}}}


{{{y=2x/5-4/5}}}   ANSWER in slope-intercept form.  m=2/5 and y-intercept=-4/5


Step 7.  See if the other point (2,0) or x=2 and y=0 satisfies this equation


{{{y=2x/5-4/5}}}


{{{0=2*2/5-4/5}}}


{{{0=0}}}  So the point (2,0) satisfies the equation and is on the line.  In other words, you can use the other point to check your work.


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


{{{2x-5y=4}}}


See graph below to check the above steps.


*[invoke describe_linear_equation 2, -5, 4]


I hope the above steps were helpful. 

 
And good luck in your studies!


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Respectfully,
Dr J