Question 224547
Find an equation of the line containing the given pair of points. (4,2), (12,6)


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=4, y1=2, x2=12 and y2=6 (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=(6-2)/(12-4)}}}


{{{m=4/8=1/2}}}


Step 4.  The slope is calculated as {{{1/2}}} or {{{m=1/2}}}


Step 5.  Now use the slope equation of Step 2 and choose one of the given points.  I'll choose point (4,2).   Letting y=y2 and x=x2 and substituting {{{m=1/2}}} in the slope equation given as,


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



{{{ 1/2=(y-2)/(x-4)}}}


Step 6.  Multiply both sides of equation by x-4 to get rid of denomination found on the right side of the equation



{{{ (x-4)/2=(x-4)(y-2)/(x-4)}}}



{{{ (x-4)/2=y-2}}}



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


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


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


Add 2 from both sides of the equation


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


{{{x/2=y}}}


{{{y=x/2}}}   This is in slope-intercept form where the slope m=1/2 and y-intercept b=0


Step 8.  See if the other point (12,6) or x=12 and y=6 satisfies this equation


{{{y=x/2}}}


{{{6=12/2}}}


{{{6=6}}}  So the point (12,6) 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/2}}}


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


{{{-x+2y=0}}}


See graph below to check the above steps.


*[invoke describe_linear_equation -1, 2, 0]


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J