Question

The equation of the line joining the origin to the point \[\left( { - 4,{\rm{ }}5} \right)\]is [MP PET \[1984\]]
A) \[5x + 4y = 0\;\;\]
B) \[3x + 4y = 2\]
C) \[5x - 4y = 0\;\]
D) \[4x - 5y = 0\]

Answer 1

Hint: Straight line is a set of infinites points in which all points are linear. Slope of the required line is calculated by using the coordinate of two points. Now, after that two points formula is used to find required equation of straight line.



Formula Used:\[m = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}\]
Where
m is slope of required line
Equation of line
\[y - {y_1} = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}\left( {x - {x_1}} \right)\]



Complete step by step solution:Given: Lines passes through origin and \[\left( { - 4,{\rm{ }}5} \right)\]
Equation of a required straight line:
\[m = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}\]
\[y - {y_1} = \dfrac{{\left( {{y_2} - {y_1}} \right)}}{{\left( {{x_2} - {x_1}} \right)}}\left( {x - {x_1}} \right)\]
Where \[\left( {{x_1},\;{y_1}} \right)\], \[\left( {{x_2},\;{y_2}} \right)\] are two points through which line passes.
\[y = \dfrac{{\left( 5 \right)}}{{\left( { - 4} \right)}}\left( x \right)\] Because line passes through origin
\[ - 4y = 5x\]
\[5x + 4y = 0\]



Option ‘A’ is correct

Note:Here use only two points equation because two points are given through which line is passes. Slope is found by using two points which is lying on lines.