# Finding the relationship between two graphs

• 02-29-2012, 04:26 AM
katpul
Finding the relationship between two graphs
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.
• 02-29-2012, 04:58 AM
pappus
Quote:

Originally Posted by katpul
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 [TEX]l_1[/TEX] and [TEX]l_2[/TEX] have the slopes [TEX]m_1[/TEX] and [TEX]m_2[/TEX] respectively and the slopes have the property:

[TEX]m_1 \cdot m_2 = -1[/TEX]

then the lines are perpendicular to each other:

[TEX]m_1 \cdot m_2 = -1~\implies~l_1\ \perp \ l_2[/TEX]
• 02-29-2012, 05:03 AM
wjm11
Quote:

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.
• 02-29-2012, 12:57 PM
katpul
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