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Question 557096: 0.03x + 0.06y=120
graph the equation by plotting points...be sure to find and show x and y intercepts.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given to graph:
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We can make our life a little easier if we get rid of the decimals by multiplying both sides (all the terms) by 100. This does not change the relationships in equation since we are doing the same multiplication on both sides. When we multiply both sides by 100 the equation becomes:
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We can now change this to the slope-intercept form of:
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in which m (the multiplier of x) is the slope of the graph and b is the value at which the graph crosses the y-axis. (In other words, b is the y-intercept.)
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To get the equation into the slope-intercept form we can begin by getting the y term by itself on the left side. This can be done by subtracting 3x from both sides to get:
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Next we can divide both sides (all terms) by 6 so that we have:
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and this simplifies to:
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This tells us a lot about the graph. First, we see that b (the constant on the right side) is +2000. Therefore, we know that the graph intercepts the y-axis at 2000. Next we see that sign on the x term is negative. That means that the graph slopes downward as it goes toward the right side of the graph. Finally, we know that the slope is 1/2, meaning that for every 2 units you go toward the right in the horizontal x direction the graph goes down 1 unit in the vertical y direction. (In this case because of the size of the units on the axes, it is probably better to think of it as for every 2000 units you go horizontally to the right, the graph will go down 1000 units vertically.)
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So we now know the y-intercept and the fact that the graph goes down as you move to the right. We don't know the x-intercept. How do we find it. Think about graphing in general. Whenever we have a point on the x-axis, what is its corresponding y-value. The y-value of a coordinate point on the x-axis is zero. So to find the x-axis intercept, all we need to do is to go to our equation, set the y-value at zero, and then solve for x. Our equation is:
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Setting the value of y at zero, the equation becomes:
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We can move the -(1/2)*x term to the left side of the equation by adding +(1/2)*x to both sides to cancel the -(1/2)*x term on the right side. We end up with:
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To solve for x, we now multiply both sides by 2 to get the answer:
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This is the x-intercept, the point on the x-axis where the graph crosses. You can now sketch the graph quickly by marking +2000 on the y-axis, then marking +4000 on the x-axis, and finally drawing an extended line through these two intercepts. The graph will be at the slope of -1/2 and will go downward as you move to the right. It will look as follows:
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The units on the axes are in thousands. So the y-intercept is actually 2000 and the x-intercept is actually 4000.
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Hope this helps you to understand this problem and some processes that you can use to solve it.
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