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Question 124433This question is from textbook Introductory Algebra
: Find an equation of the line that has the same y-intercept as the line x - 3y = 6 and contains the point (5,-1).
This question is from textbook Introductory Algebra
Found 2 solutions by ilana, checkley71:
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! I am guessing you have learned the point-slope form of a linear equation, y-y1=m(x-x1), where m is the slope and (x1,x2) is the point. So, for your line, x1=5 and y1=-1. That means we just need m. We have the equation x-3y=6, but that does not immediately tell us the slope. But do you remember the first form of a linear equation you learned? It was probably y=mx+b, where m is the slope. This equation is very close to that, so let's just play with it until it looks exact, and then we'll see m, the slope.
First get the y term alone: -3y=6-x
Now divide by -3: y=-2+(1/3)x
Switch the terms so the x term is before the constant: y=(1/3)x-2
m=1/3
So we have a point and a slope- put it into the form at the beginning.
y+1=(1/3)(x-5)
This can also be written y+1=(x-5)/3
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website! X-3Y=6
-3Y=-X+6
Y=-X/-3+6/-3
Y=X/3-2 [-2 IS THE Y INTERCEPT.] (RED LINE)
NOW WE HAVE 2 POINTS (0,-2) & (5,-1)
THIS SLOPE=(-1+2 )/(5-0)=1/5
THUS THIS LINE EQUATION WITH A SLOPE=1/5, A Y INTERCEPT OF (0,-2) & PASSING THROUGH (5,-1) IS:
Y=X/5-2 (GREEN LINE)
 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = x/3 -2 and y = x/5 -2).
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