Question 216340
How do I find the slope of 5x-2y=10?


Step 1.  To find the slope of this equation in standard form you need to change it to slope intercept form given as y=mx+b where m is the slope and the y-intercept is b when x=0 and at point (0,b).


Step 2.  Take equation {{{5x-2y=10}}} in standard form and put in slope-intercept form


{{{5x-2y=10}}}


Add 2y-10 to both sides of the equation


{{{5x-2y+2y-10=10+2y-10}}}


{{{5x-10=2y}}}


Divide 2 to both sides of the equation


{{{5x/2-10/2=2y/2}}}


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


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


Step 3. ANSWER:  The equation {{{y=5x/2-5}}}  is in slope-intercept form where the slope m=5/2 and slope-intercept b=-5 at (0,-5).


The graph of this line is shown below.  Note the slope m=5/2 (which means 2 horizontal steps to the right will result in 5 vertical steps up).  Also note the y-intercept b=-5 at x=0 at point (0,-5)


{{{graph(400,400, -10,10,-10,10, 5x/2-5)}}}


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 Trigonmetry 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