Question

Let there be a line m passing through the points $(8,6)$ and $(7,11)$ in the $xy$ plane. Let there be another n line in the same plane having a slope $-3$ and $x$ intercept as $2$. Find the $y$ coordinate of the point of intersection of the lines m and n.

• A. $-\frac{54}{5}$
• B. $\frac{54}{5}$
• C. $55$
• D. $-54$

Answer 1

The correct option is D $-54$

Given line m is passing through points $(8,6)$ and $(7,11)$

Equation of line $m:y-6=\frac{11-6}{7-8}(x-8)$

$m:y-6=\frac{-5}{1}(x-8)$

$m:y-6=-5x+40$

$m:5x+y=46$

Equation of line n with slope $-3$ and x intercept $2$

$n:y=-3(x-2)$

$n:y=-3x+6$

$n:y=-3x+6$

$n:3x+y=6$

On solving eq m and n we get

$3\left(\frac{46-y}{5}\right)+y=6$

$138-3y+5y=30$

$2y=30-138$

$2y=-108\Rightarrow y=-54$