Question 217334
Point  Slope 
(5, 2)  m = -2 

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope.


Step 1.  The slope intercept form is given at y=mx+b where m is the slope and b is the y-intercept when x=0 and at point (0,b).


Step 2.  Given m=-2, then {{{y=-2x+b}}}.  But the point (5,2) or x=5 and y=2 must lie on the line.  So we can use it to find the y-intercept b.


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


{{{2=-2*5+b}}}


{{{2=-10+b}}}


Add 10 to both sides of the equation to get b.


{{{2+10=-10+b+10}}}


{{{12=b}}}


Step 3.  ANSWER:  {{{y=-2x+12}}}


The graph of the line in Step 3 is shown below.  Note the y-intercept b=12 at x=0 and the line passes through (5,2).  Slope m=-2 such that one unit to the left is two units  down.


{{{graph(600,600, -15,15, -15,15, -2x+12)}}}


I hope the above steps and explanation were helpful. 


For Step-By-Step videos on Introduction to Algebra, 

please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and 

for Trigonometry please visit 

http://www.FreedomUniversity.TV/courses/Trigonometry. 


Also, good luck in your studies and contact me at 

john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J