Question

A straight line passes through points $A(2,-4)$ and $B(3,-2)$. find the
I) slope of the line
ii) Equation of the line $AB$
iii) value of $p$, if $AB$ passes through the point $(P+1,p-3)$.

Answer 1

Given striaght the paints A(2,-4) B(3,-2)

(i) slope of AB $=\frac{-2+4}{3-2}=\frac{2}{1}=2$

(ii) line y+2 = 2 (x-3)

y+2 = 2x-6

$\Rightarrow 2x-y-8=0$

(iii) Given (P+1,P-3) lies on line

2(P+1)-(P-3)-8 = 0

2P+2-P+3-8 = 0 $\Rightarrow P-3=0$

$\Rightarrow P=3$