+845 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.
+343 \(7𝑥 + 2𝑦 = 11 \)
\(<=> 𝑦 =- \frac{7x}{2} + \frac{11}{2}\)
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)
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