Question

The equation of a line through the intersection of lines $x=0$and $y=0$ and through the point $(2,2)$ is:

• A. $y=x-1$
• B. $y=-x$
• C. $y=x$
• D. $y=-x+2$

Answer 1

The correct option is C

$y=x$

Determine the equation of the line :

Let the required line be $AB$.

Given that: $AB$ passes through the point $(2,2)$ and through the intersection of the lines $x=0$ and $y=0$ .

Point of intersection of $x=0$ and $y=0$ is $(0,0)$.

So, now we have to find the equation of the line that passes through the point $(0,0)$ and $(2,2)$.

Slope of $AB$ :

$\begin{array}{rcl}& =& \frac{y_2-y_1}{x_2-x_1}\\ & =& \frac{2}{2}\\ & =& 1\end{array}$

Equation of $AB$:

$$\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-0=1(x-0) \\ \Rightarrow y=x \end{gathered}$$

Hence, the correct answer is Option (C).