SOLUTION: Write the equation of the line passing through (3, -3) and (3,-6) Which is the ordered pairs (0,0) (-2, 10), (-1,-5), (-3,9) are solutions for the equation y=5x?

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line passing through (3, -3) and (3,-6) Which is the ordered pairs (0,0) (-2, 10), (-1,-5), (-3,9) are solutions for the equation y=5x?      Log On


   

Question 110757: Write the equation of the line passing through (3, -3) and (3,-6)
Which is the ordered pairs (0,0) (-2, 10), (-1,-5), (-3,9) are solutions for the equation y=5x?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (3,-3) and (3,-6)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (3,-3) and (x%5B2%5D,y%5B2%5D) is the second point (3,-6))


m=%28-6--3%29%2F%283-3%29 Plug in y%5B2%5D=-6,y%5B1%5D=-3,x%5B2%5D=3,x%5B1%5D=3 (these are the coordinates of given points)


m=+-3%2F0 Subtract the terms in the numerator -6--3 to get -3. Subtract the terms in the denominator 3-3 to get 0




Since the denominator is zero, the slope is undefined (remember you cannot divide by zero). So we cannot use the slope intercept form to write an equation. So we can only say that the equation is a vertical line through x=3, which means the equation is x=3 (notice this is not in slope-intercept form)



So the equation x=3 looks like this:

Graph of x=3 through the points (3,-3) and (3,-6)





#2


y=5%2Ax Start with the given equation


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


%280%29=5%2A%280%29 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%2Ax



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



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


%2810%29=5%2A%28-2%29 Plug in x=-2 and y=10


10=-10 Simplify. Since the two sides of the equation are not equal, this means (-2,10) is not a solution to y=5%2Ax



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



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


%28-5%29=5%2A%28-1%29 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%2Ax



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



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


%289%29=5%2A%28-3%29 Plug in x=-3 and y=9


9=-15 Simplify. Since the two sides of the equation are not equal, this means (-3,9) is not a solution to y=5%2Ax


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Answer:
So the following ordered pairs are solutions to y=5%2Ax

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

Now let's graph the equation y=5%2Ax and plot the points (0,0), (-2,10), (-1,-5), and (-3,9)

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%2Ax.
Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation y=5%2Ax