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

#1**+1 **

\(7𝑥 + 2𝑦 = 11 \)

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

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