Question 466393: solve the equation for y, (I am not to use any mixed number is my answer). Then I must find three solutions for the equation and graph it.
6y + 11x = -11
My first step is to isolate y, so therefore I believe I need to take away 11x from both sides.
Which leaves me with 6y = -11 - 11x and then I need to divide by 6
this is where i get confused. y = -11/6 - 11/6 x Im unclear as to this step
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have the right idea.
your equation is:
6y + 11x = -11
subtract 11x from both sides of the equation to get:
6y = -11x - 11
divide both sides of the equation by 6 to get:
y = (-11x/6) - (11/6)
this can also be written as:
y = (-11/6)*x - (11/6)
your equation is now in the slope intercept form of the equation of a straight line.
the slope is equal to (-11/6) and the y intercept is equal to -(11/6)
you now need to find 3 values of x that will result in 3 values of y and then you need to graph the 3 points.
they will form a straight line.
pick x = 0 as your first number.
you will get:
when x = 0, y = -(11/6)
pick x = 1 as your second number.
you will get:
when x = 1, y = (-11/6)*1 - (11/6) which becomes y = (-11/6) - (11/6) which becomes y = (-11-11)/6 which becomes (-22/6).
pick x = 2 as your third number.
when x = 2, y = (-11/6)*2 -(11/6) which becomes y = (-22/6) - (11/6) which becomes y = (-22-11)/6 which becomes y = (-33/6).
you have 3 points.
you graph these 3 point pairs.
they are:
(x,y) equals:
(0,-11/6)
(1,-22/6)
(2,-33/6)
a graph of your equation looks like this:
notice that when x = -1, y = 0
that give you 4 points to explore.
they are:
(x,y) equals:
(-1,0)
(0,-11/6)
(1,-22/6)
(2,-33/6)
notice that when x moves up 1, y moves down 11/6.
that's because the slope of the equation is (-11/6)
the slope is the change in the value of y divided by the change in the value of x.
y goes down 11/6 units every time x goes up 1 unit.
that's a slope of (-11/6) / 1 which equals (-11/6).
if i didn't mention it before, the general form of the slope intercept form of the equation of a straight line is:
y = mx + b
m equals the slope
b equals the y intercept (value of y when x = 0)
your equation is:
y = -(11/6)x - (11/6)
m = slope = -(11/6)
b = y intercept = value of y when x = 0 = -(11/6)
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