Question 116250


{{{y=5*x}}} Start with the given equation



Let's test the first solution (0,0):



{{{(0)=5*(0)}}} Plug in {{{x=0}}} and  {{{y=0}}}



{{{0=0}}} Simplify. Since the two sides of the equation are equal, this means (0,0) is a solution to {{{y=5*x}}}




-------Now lets test another solution-------




Let's test the second solution (-2,10):



{{{(10)=5*(-2)}}} Plug in {{{x=-2}}} and  {{{y=10}}}



{{{10=-10}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-2,10) is <font size=4><b>not</b></font> a solution to {{{y=5*x}}}




-------Now lets test another solution-------




Let's test the third solution (-1,-5):



{{{(-5)=5*(-1)}}} Plug in {{{x=-1}}} and  {{{y=-5}}}



{{{-5=-5}}} Simplify. Since the two sides of the equation are equal, this means (-1,-5) is a solution to {{{y=5*x}}}




-------Now lets test another solution-------




Let's test the fourth solution (-3,9):



{{{(9)=5*(-3)}}} Plug in {{{x=-3}}} and  {{{y=9}}}



{{{9=-15}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (-3,9) is <font size=4><b>not</b></font> a solution to {{{y=5*x}}}



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Answer:

So the following ordered pairs are solutions to {{{y=5*x}}}


(0,0) and  (-1,-5) 


Now let's graph the equation {{{y=5*x}}} and plot the points (0,0), (-2,10), (-1,-5), and (-3,9)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,5*x),

circle(0,0,0.08),
circle(0,0,0.10),
circle(-2,10,0.08),
circle(-2,10,0.10),
circle(-1,-5,0.08),
circle(-1,-5,0.10),
circle(-3,9,0.08),
circle(-3,9,0.10),
green(circle(0,0,0.05)),
green(circle(0,0,0.08)),
green(circle(-1,-5,0.05)),
green(circle(-1,-5,0.08)))}}}

Here we can see that the points (0,0) and  (-1,-5)  lie on the line (they are the green points). These are the solutions to the equation {{{y=5*x}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{y=5*x}}}