Question 237273: given the equation 3x+y=6
a.) what are the x and y intercepts? show your calculations
b.) on the graph at the right draw the equation using the x and y intercepts.
c.) does the line you drew in b have a positive slope, a negative slope, zero slope or no slope? you should not have to do any calculations to answer this question.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 3x+y=6
First, let x=0 and find y.
3(0) +y=6
y=6 This is the y intercept.
Next, let y=0 and find x.
3x + 0 = 6
3x=6
x=2. This is the x intercept.
Graph these points, and connect the dots, and it should look like this:
 .
From this graph, you can probably see that the slope of the graph is NEGATIVE.
You can also find the slope of the line, by solving the original equation for y by subtracting 3x from each side. You get y=-3x+6. From this, the coefficient of x gives you the slope, so the slope is m=-3, which as you can see is a NEGATIVE SLOPE!
If you need more help on this topic of Graphing a Straight Line, please see my own website for my "non-traditional" explanation. Do a "Bing" or "Google" search for my last name "Rapalje". Near the top of the search list, look for "Rapalje Homepage." Near the top of my Homepage, look for the link "Basic, Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look in Chapter 4 for the sections on Graphing and Slope of a Line.
In addition, I have a complete explanation of me teaching this topic on a FREE video on my website. From the Homepage of my website, look for the link "Rapalje Videos in Living Color". Select "Basic Algebra" and look for the topic "Graphing and Slope of the Line." If you like the website and the videos that I have here, please recommend them to family and friends. Everything is FREE, just like algebra.com!!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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