Question

Straight line passing through the points $(-1,1),(0,0)$and $(1,-1)$ has equation.

• A. $y=x$
• B. $x+y=0$
• C. $y=2x$
• D. $2+3y=7x$

Answer 1

The correct option is B

$x+y=0$

To determine the equation of line passing through the points $(-1,1),(0,0)$ and $(1,-1)$

We know that the equation of a line is given by $y=mx+c$.

Hence we need to find the value of $m$and $c$, to obtain the equation.

Step 1: Calculating $m$

We know $m$ is the slope of a line and slope of a point passing through any two points is given by

$m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Let the points taken to determine $m$ be $(-1,1)$ and $(1,-1)$

Substituting the values we get,

$$\begin{gathered} m=\frac{(-1)-1}{1-(-1)} \\ m=\frac{-2}{2} \\ m=-1 \end{gathered}$$

Therefore, the slope of the line $m$ is $-1$

Step 2: Determine $c$ using the slope $m$and any one of the given points

Let us use the point $(0,0)$

We know the equation of line is given by $y=mx+c$

Therefore substituting the values $x=0,y=0,m=-1$

Thus we get $0=-1\times 0+c$

$c=0$

Thus the y-intercept is $0$

Step 3: Finding the equation

Substituting all the calculated values in the equation $y=mx+c$, to obtain the equation of line.

$y=mx+c$

$y=(-1)x+0$

$y=-x$

$y+x=0$

Thus the equation of the line is $x+y=0$

Hence the correct option is B.