<s>[INST] Through the point $A(4,5)$ a line is drawn. Through the point $A(4,5)$ a line is drawn inclined at $45°$ with the $+ve$ X - axis. It meets $x+y=6$ at the point $B$. Find the equation of $AB$.
My solution..
Equation of $AB$ 
$$(y-y_1)=m(x-x_1)$$
$$(y-5)=1(x-4)$$
$$x-y+1=0$$.
But the answer in my book is $3x-y=7$.
Can anyone tell me where I made mistake?.
 [/INST] The equation of the first line is: $y - 5 = \tan(45^{\circ})(x - 4)= 1(x-4) = x-4\Rightarrow y = 5+x-4 = x+1$. Thus the intersection is found by:  $x + 1 = 6- x \Rightarrow x = \dfrac{5}{2}\Rightarrow y = 6 - \dfrac{5}{2} = \dfrac{7}{2}\Rightarrow B = (\frac{5}{2}, \frac{7}{2})$. Can you take it from here?
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