The equation of a line through the intersection of lines $x=0$ and $y=0$ and through the point $\left( 2,~2 \right)$ is (a) $y=x-1$ (a) $y=-x$ (b) $y=x$ (c) $y=-x+2$
Answer
Verified
Hint: Substitute the given points into the standard equation of line formula.
The equations of the given lines are $x=0$ and $y=0$. The coordinates of the point of intersections are already available. This means that the point of intersection of these lines would be $\left( 0,0 \right)$. Another point through which the required line passes through is given in the question as $\left( 2,2 \right)$. Now, we know that the equation of a line passing through two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] is given by, \[\begin{align} & y-{{y}_{1}}=m(x-{{x}_{1}}) \\ & \Rightarrow y-{{y}_{1}}=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\times (x-{{x}_{1}}) \\ \end{align}\] So, the equation of the required line passing through $\left( 0,0 \right)$ and $\left( 2,2 \right)$ can be obtained as, $y-0=\dfrac{2-0}{2-0}\left( x-0 \right)$ Therefore, the equation of the required line is $y=x$. Hence, we get option (c) as the correct answer.
Note: The equations $x=0$ and $y=0$ indicate that the required line passes through the origin. So, the formula to find the equation of the line passing through a point $\left( {{x}_{1}},{{y}_{1}} \right)$ can be obtained as $y=mx$, where $m=\dfrac{{{y}_{1}}}{{{x}_{1}}}$ is the slope.
×
Sorry!, This page is not available for now to bookmark.