Question

Which lines pass through point $\left( 3,-8 \right)$ ?
(a). $3x-6y=48$
(b). $9x+2y=1$
(c). $7x-3y=45$
(d). $8x-3y=0$

Answer 1

Hint: First, here only one point is provided to us so it can be solved by putting those points in the option and comparing left-hand side (LHS) and right-hand side (RHS). If both get equal then that is our required line which passes through the point $\left( 3,-8 \right)$ .

Complete step-by-step answer:

In the question, we are given a pair of points and we have to find which line will pass through this point.
So, we have a point $\left( 3,-8 \right)$ which is represented as $\left( x,y \right)$ . Now substituting this value in the all the option and comparing the right-hand side (RHS) of the equation.
Now, taking option(a): $3x-6y=48$ So, taking left-hand side (LHS) and substituting $\left( 3,-8 \right)$ we get,
LHS $=3x-6y$
$=3\left( 3 \right)-6\left( -8 \right)$
$=9+48=57$
Therefore, LHS is 57 and RHS is given as 48 which is not equal. So, this option is not correct.
Similarly, taking option(b): $9x+2y=1$ substituting the point $\left( 3,-8 \right)$ in LHS and comparing with RHS we get,
LHS $=9\left( 3 \right)+2\left( -8 \right)$
$=27-16=11$
So, LHS is 11 and RHS is 1 which is not equal. Thus, this option is also not correct.
Now, taking option(c): $7x-3y=45$ substituting the point $\left( 3,-8 \right)$ in LHS and comparing with RHS we get,
LHS $=7\left( 3 \right)-3\left( -8 \right)$
$=21+24=45$
So, LHS is 45 and RHS is 45. Thus, both are equal, so this option is correct.
Now, taking option(d): $8x+3y=0$ substituting the point $\left( 3,-8 \right)$ in LHS and comparing with RHS we get,
LHS $=8x-3y=0$
$=24+24=48$
So, LHS is 48 and RHS is 0. Thus, both are not equal, so this option is not correct.
Thus, option (c) is the correct answer.

Note: Another approach to solve this type of question is considering two pair of points i.e. $\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ which is $\left( 3,-8 \right),\left( 0,0 \right)$ and substituting the value in the formula $\dfrac{x-{{x}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\dfrac{y-{{y}_{1}}}{{{y}_{2}}-{{y}_{1}}}$. So, we get
$\dfrac{x-{{x}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\dfrac{y-{{y}_{1}}}{{{y}_{2}}-{{y}_{1}}}\Rightarrow \dfrac{x-3}{0-3}=\dfrac{y-\left( -8 \right)}{0-\left( -8 \right)}$
$\Rightarrow \dfrac{x-3}{-3}=\dfrac{y+8}{8}$
$\Rightarrow 8\left( x-3 \right)=-3\left( y+8 \right)$
$\Rightarrow 8x-24=-3y-24$
On simplifying, we get
$\Rightarrow 8x+3y=0$ Thus, we get a different answer. But this is not given in any option, so this is not the correct answer also the second pair of points are not given to us. We just assumed to be 0.