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Question 574731: what is the slope of the line of the equation y+3x=6
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! There is a conventional form for a linear equation called the slope-intercept form. The form of this equation is:
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y = m*x + b
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and in this equation the m which is the multiplier of x is the slope of the line that is the graph of the equation. And the b is a constant that is the value on the y-axis where the line graph crosses the y-axis.
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So let's start with the given equation y + 3x = 6 and see if we can't get it into the same form as the slope-intercept form. We do this as follows:
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Start with the given equation:
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y + 3*x = 6
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Move the +3*x to the right side by subtracting 3*x from (or adding negative 3*x to) both sides:
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y + 3*x - 3*x = -3*x + 6
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On the left side the 3*x and the -3*x cancel each other and we are left with:
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y = -3*x + 6
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If you compare this with the slope-intercept form you can now see that the multiplier of the x is -3, and since the multiplier of the x is the slope, we then know that the slope of the line graph is -3. And in addition, we know that the line graph crosses the y-axis where y equals +6.
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Hope this helps you to understand this problem a little better. The slope-intercept form of the equation is a very useful form to work with in graphing.
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