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# The line AB has equation 7𝑥 + 2𝑦 = 11

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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