Question

Write an equation of a line with an $x$-intercept of $2$.

Short answer

One of the required equation is $y=x-2$.

Step-by-step solution

– Equation of line.

The graph of linear equation is always a straight line. The slope intercept form of a linear equation is:

$y=mx+b$ …(i)

Where m is the slope and b is the y-intercept.

– Given information.

The x-intercept of the required line is 2. It means the line passes through the point $\left(2,0\right)$.

– Write a linear equation.

Substitute $x=2,y=0$in (i).

$\begin{array}{c}0=m\left(2\right)+b\\ -b=2m\end{array}$

Let m=1, then

$\begin{array}{c}-b=2\left(1\right)\\ -b=2\\ b=-2\end{array}$

Substitute $m=1,b=-2$in (i).

$\begin{array}{l}y=\left(1\right)x+(-2)\\ y=x-2\end{array}$

Thus, one of the required equation is $y=x-2$.