Question 127565
Equation: {{{5x + 2y = 10}}}

a. Solve the equation for {{{y}}} and sketch the graph.

{{{5x + 2y = 10}}}.........move {{{5x}}} to the right

{{{2y = -5x +10}}}......divide both sides by {{{2}}}

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

graph:

{{{ graph( 300, 200, -6, 5, -10, 10, -(5/2)x + 5) }}}


b. Multiply the equation {{{5x + 2y = 10}}}by {{{3}}}, and then solve 
for{{{ y}}}. 
How does the graph of this equation compare with the graph of the original equation? Explain your answer. 

{{{5x*3 + 2*3y = 10*3}}}

{{{15x + 6y = 30}}}

{{{ 6y = -15x + 30}}}

{{{ y = -(15/6)x + 30/6}}}

{{{ y = -(cross(15)*5/cross(6)2)x + 5}}}

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

{{{ graph( 300, 200, -6, 5, -10, 10, -(5/2)x + 5) }}}


 the graph of this equation is same as the graph of the original equation; we did multiply equation by {{{3}}}, but in order to solve it for {{{y}}} we needed to divide by {{{3}}}too
or, if we use this property {{{(a*b)/b=a}}} our equation will not change