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Write the equation of a line which passes through (3,5) and is perpendicular to y=(3/4)x6 in slopeintercept form.
 11 months ago
 11 months ago
Write the equation of a line which passes through (3,5) and is perpendicular to y=(3/4)x6 in slopeintercept form.
 11 months ago
 11 months ago

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e.mccormickBest ResponseYou've already chosen the best response.1
First, do you know the method to find the slope of a perpendicular line?
 11 months ago

telijahmedBest ResponseYou've already chosen the best response.0
dw:1369021818640:dw
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
Not in this case. The perpendicular is the negative inverse of the slope of the given line. Do you know what that is?
 11 months ago

telijahmedBest ResponseYou've already chosen the best response.0
dw:1369021841094:dw
 11 months ago

telijahmedBest ResponseYou've already chosen the best response.0
dw:1369021901093:dw
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
Oh ok i always get those two confused.
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
if slope of ur given line is \[m _{1}\]
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
So, what would the slope of the perpendicular line be in this case?
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
then \[m _{1}=\frac{ 3 }{ 4 }\]
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
if the slope of a perpendicular line is \[m _{2}\]
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
Ok is the equation to find out what the perpendicular line y=mx+b or m=y^2  y^1 / x^2x^1?
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
then\[m _{1}m _{2}=1\]
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
or\[\frac{ 3 }{ 4 }m _{2}=1\]
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
We need the slope first. shamim has pointed out the slope of the original line. Do you know what is meant by the "negative inverse" of that?
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
The negative opposite?
 11 months ago

shamimBest ResponseYou've already chosen the best response.0
\[m _{2}=\frac{ 4 }{ 3 }\]
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
Well, inverse is sort of opposite. If you mean inverse as in \(\frac{a}{b}\implies \frac{b}{a}\) is the inverse.
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
Alright, so in order to find the slope we use y=mx+b right?
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
To invert is to turn upside down or reverse position. That is where inverse comes from. Just some simple language, but they make it sound cryptic by tossing it into math. No, shamim went ahead and posted it. All you needed was the m part of the original line. Do you see the \(m_2\)?
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
Yes, i see. So next up would be to use the y^2y^1 equation?
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
So in this case (3,5) would be (x^1,y^1) while −4/3 would be (x^2,y^2)?
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
No, 4/3 is m. You just need that and one point.
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
\(yy_1=m(xx_1)\)
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
y5 = 4/3(x3) is that right so far?
 11 months ago

CSmith17Best ResponseYou've already chosen the best response.0
And that would be the final answer correct?
 11 months ago

e.mccormickBest ResponseYou've already chosen the best response.1
This became a bit of a posting mess and then the site went down, so here is a summary of what was done: You were given the line \(y=\frac{3}{4}x6 \) and point \((3,5)\) with the instructions to find the slopeintercept equation of the perpendicular line through that point. First, you need the slope of the line being found. The perpendicular line has the negative inverse slope of the given line. To invert is to turn upside down or reverse position and negative is the mathematical changing of sign from \(+\) to \(\) or \(\) to \(+\). If you understand the concept, you flip it and make it the opposite sign. However, here is the mathematical way to find the slope of the perpendicular line: Start with the original line, \(y=\frac{3}{4}x6 \). Form that you get \(m_1\). The negative inverse implies that if they were multiplied, the result would be 1. That is stated as: \(m_1m_2=1\) and put what is known, \(m_1\) into that: \(\frac{3}{4}m_2=1\) Then solve for \(m_2\) \(\frac{3}{4}m_2=1\) \(\frac{4}{3}\cdot\frac{3}{4}m_2=\frac{4}{3}\cdot1\) \(m_2=\frac{4}{3}\) So \(m_2=\frac{4}{3}\) becomes just m for the new formula, the pointslope version of a line. Point slope lets you use any point and the slope to find the formula of a line: \(yy_1=m(xx_1)\) \(yy_1=\frac{4}{3}(xx_1)\) Then we toss in the point \((3,5)\): \(y5=\frac{4}{3}(x3)\) That is a formula for the line, but they wanted a specific formula, the slopeintercept version. To get that, you need to solve for y. \(y5=\frac{4}{3}(x3)\) \(y5=\frac{4}{3}x+4\) \(y5+5=\frac{4}{3}x+4+5\) \(y=\frac{4}{3}x+9\) And there it is! The slopeintercept equation of the perpendicular line through the given point.
 11 months ago
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