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The line AB has equation 7𝑥 + 2𝑦 = 11

The point C has coordinates (-5, 25/2 )

Find an equation of the line which passes through C and is parallel to the line AB

Given the line AB passes through the point (k, k+1) find the value of the constant k.

YEEEEEET  Oct 28, 2018
edited by YEEEEEET  Oct 29, 2018
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\(7𝑥 + 2𝑦 = 11 \)

\(<=> 𝑦 =- \frac{7x}{2} + \frac{11}{2}\)

We will call \(λ=-7/2 \) is the coefficient of x 

so every parallel line to AB will have \(λ=-7/2\)

lines have type : \(y-y1=λ(x-x1) \) We want coordinates (-5, 25/2 ) 

so x1=-5 and y1=(25/2) 

\(y-(\frac{25}{2})=-\frac{7}{2}(x-(-5))\)

\(y=-\frac{7}{2}(x+5))+\frac{25}{2}\)

\(y=-\frac{7}{2}x-\frac{35}{2}+\frac{25}{2}\)

\(y=-\frac{7}{2}x-\frac{10}{2}\)

\(7x+ 2y=-10\)

 

"Given the line AB passes through the point (k, k+1) find the value of the constant k."

This means  x= k, y=k+1 verify the equation 7𝑥 + 2𝑦 = 11 

So 

\(7k+2(k+1)=11 \)

\(7k+2k+2=11 \)

\(9k=9\)

so \(k=1\) 

Finally the point (k, k+1) is (1,2) 

Help its helps! 

Dimitristhym  Oct 29, 2018

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