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Question 255227: 7r-6s=-22
6r+7s=54
solve.
i think i need coordinates so i can graph it. if that makes any sense.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equations are:
7r - 6s = -22
6r + 7s = 54
if you let:
y = s and x = r, your equations become:
7x - 6y = -22
6x + 7y = 54
now you can graph them on an xy plane where x is the horizontal axis and y is the vertical axis.
in order to graph them, you have to solve for y in both equations.
first equation becomes y = (7/6)x + (22/6)
second equation becomes y = -(6/7)x + (54/7)
graph of these equations looks like this:
to graph them manually, you would need coordinates, but you would only need 2 for each equation since they are straight lines.
if you let x = 0, one of the coordinates pops up easily.
then just pick any other value for x, like 5 or 10, and you get your second coordinate.
then just draw a straight line passing through those 2 points.
these equations are perpendicular to each other.
after you solved for y, they are in slope intercept form.
slope intercept form is y = mx + b where m is the slope and b is the y-intercept.
y-intercept is the value of y when x = 0.
slope for the first equation is (7/6).
slope for he second equation is -(6/7).
negative reciprocal of (7/6) is -(6/7) telling you that these lines are [perpendicular to each other.
the form that they started off in is the standard form of the equation of a straight line which is ax + by = c
if you graph them manually, you could keep them as r and s.
just make r the horizontal axis and s the vertical axis.
I had to convert them to x and y because the graphing function required them to be x and y.
keeping them as r and s, then the slope intercept form of the equations is:
s = (7/6)r + (22/6)
s = -(6/7)r + (54/7)
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