Finding the relationship between two graphs

katpul

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Feb 29, 2012
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I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.
 
I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.

It's guessing on my side, but:

If two lines \(\displaystyle l_1\) and \(\displaystyle l_2\) have the slopes \(\displaystyle m_1\) and \(\displaystyle m_2\) respectively and the slopes have the property:

\(\displaystyle m_1 \cdot m_2 = -1\)

then the lines are perpendicular to each other:

\(\displaystyle m_1 \cdot m_2 = -1~\implies~l_1\ \perp \ l_2\)
 
I have two graphs g(x) = -2x-3 and h(x) = (1/2)x. I have graphed each linear function, found the range and domain, but I am having trouble describing the relationship between the two graphs. My original answer was that if you remove the y-intercept from g(x), the graph of h(x) is obtained by vertically shrinking g(x) and then reflecting it about the x-axis. This was wrong. Can someone help steer me in the right direction. Thanks.

Look at the slopes of the two lines: -2 and 1/2. Notice anything about these values? They are negative reciprocals of each other. Does that sound familiar? It means that the lines are perpendicular to each other.
 
Thank You

Thank you guys. This is one of those things where it is so simple and obivious I just couldn't see it. :D
 
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