Question

What is the equation of a line with an undefined slope and goes through (2, 4)?

Answer 1

Hint: We know that slope – intercept form of the equation of a straight line is equal to $y=mx+c$. And in this equation of a straight line, “m” is the slope and “c” is the y intercept. Now, we have given that the slope of the line is undefined. Then substitute the value of slope as ${\displaystyle \frac{1}{0}}$ and then cross multiply. After that, we will substitute the point (2, 4) in this straight line equation.

Complete step-by-step solution:
In the above problem, it is given that a straight line with an undefined slope and a point (2, 4) is passing through this straight line.
We know that the equation of a straight line in slope – intercept form is as follows:
$y=mx+c$
Now, in the above equation, “m” is the slope of a straight line and “c” is the y – intercept of the straight line.
It is given that slope of the straight line is undefined so substituting the slope as ${\displaystyle \frac{1}{0}}$ in the above equation we get,
$\begin{array}{rl}& y={\displaystyle \frac{1}{0}}x+c\\ & \Rightarrow x=c\end{array}$
It is given that the point (2, 4) passes through the above equation and we get,
$\begin{array}{rl}& x=c\\ & \Rightarrow 2=c\end{array}$
Substituting the value of c as 2 in $x=c$ equation we get,
$x=2$
Hence, the equation of a straight line having undefined slope and passing through the point (2, 4) is $x=2$.

Note: The alternate approach to this problem is that it is given that slope is undefined. This means that the straight line is parallel to y axis. And we know that the equation of a straight line parallel to y axis is $x=c$ where “c” is the constant. Now, to find the value of “c” substitute the point (2, 4) as the same as that we did in the above solution. In this way, we will get the equation of a straight line.