Question 229924
Find the equation of the line containing the given pair of points (-9,0) and (0,7)


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=-9, y1=0, x2=0 and y2=7 (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=(7-0)/(0-(-9))}}}


{{{m=7/9}}}


Step 4.  The slope is calculated as {{{7/9}}} or {{{m=7/9}}}


Step 5.  Now use the slope equation of Step 2 and choose one of the given points.  I'll choose point (0,7).   Letting y=y2 and x=x2 and substituting {{{m=1/2}}} in the slope equation given as,


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



{{{ 7/9=(y-7)/(x-0)}}}


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



{{{ 7x/9=cross(x)(y-7)/cross(x)}}}



{{{ 7x/9=y-7}}}


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


Add 7 to both sides of the equation


{{{7x/9+7=y-7+7}}}


{{{7x/9+7=y}}}


{{{y=7x/9+7}}}   This is in slope-intercept form where the slope m=7/9 and y-intercept b=0


Step 8.  See if the other point (-9,0) or x=-9 and y=0 satisfies this equation


{{{y=7x/9+7}}}


{{{0=7*(-9)/9+7}}}


{{{0=0}}}  So the point (-9,0) 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=7x/9+7}}}


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


{{{-7x+9y=63}}}


See graph below to check the above steps.


{{{graph(400,400, -10,10, -10,10, 7x/9+7)}}}


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J