Question

How do you find the standard form for the line with (6,7); m= undefined?

Answer 1

The standard form of the equation of a straight line is $ax+by+c=0$, here $a,b\And c\in$ Real numbers. We can find the slope of the line using the coefficients of the equation. The slope of the line in terms of coefficients equals $\dfrac{-a}{b}$.

Complete answer:
We are given that a line passes through points $(6,7)$, and its slope is undefined. We have to find the standard form of the equation of this line. Let’s say that the standard form of the equation of line is $ax+by+c=0$, we can find the values of $a,b\And c$ using the given information, as follows
The slope of this line should be $\dfrac{-a}{b}$, we are given that this value is undefined. A fraction is said to be undefined if its denominator is zero. Hence, here value of b is 0. substitute this value in the equation of line we assumed, we get

& \Rightarrow ax+0\times y+c=0 \\\ & \Rightarrow ax+c=0 \\\ \end{aligned}$$ Dividing both sides by $$a$$, we get $$\begin{aligned} & \Rightarrow ax\times \dfrac{1}{a}+c\times \dfrac{1}{a}=0\times \dfrac{1}{a} \\\ & \Rightarrow x+\dfrac{c}{a}=0 \\\ \end{aligned}$$ We know that the line passes through the point $$(6,7)$$. So, it has to satisfy the equation of the line. Substituting this point in the above equation of line. We get, $$\Rightarrow 6+\dfrac{c}{a}=0$$ Subtracting 6 from both sides of the equation, we get $$\begin{aligned} & \Rightarrow 6+\dfrac{c}{a}-6=0-6 \\\ & \Rightarrow \dfrac{c}{a}=-6 \\\ \end{aligned}$$ Substituting this value in the equation of line we made, we get $$\Rightarrow x-6=0$$ Hence the standard form of the equation is $$x-6=0$$. **Note:** It should be remembered that if the slope of the line is undefined or zero, then in that case the equation of the line is $$x-a=0$$ or $$y-a=0$$ respectively. The value of $$a$$ can be found using other information given about the line.