Question

How do you find the slope of the line $x=-7$ ?

Answer 1

We are given an equation of line as $x=-7$ . We are asked to find the slope of it, we will first learn what is slope then we focus at various method to find slope we learn what slope is then we will find it using $\tan \theta$ and also by $m=\dfrac{\text{rise}}{\text{run}}$ . we will learn about slope intercept term, we convert problem to slope intercept form then we will find the slope.

Complete step by step solution:
We are given an equation as $x=-7$ .
We are asked to find the slope of the given equation and also to find the y-intercept.
We will first understand that what is the slope means then we will focus on the ways to find the slope of any given equation.
Now, the slope of any line is the angle made by the line with the positive x-axis.
We generally find the slope by finding the ratio of rise and run.
Rise means movement of the function along the y-axis while run refers to the movement along x-axis.
So, one way in slope $=\dfrac{\text{rise}}{\text{run}}$ .
Another way is to find the term of the angle made by the line with x-axis.
So, slope $=\tan \theta$ .

Slope is denoted as ‘m’, so –
$m=\tan \theta$ or $m=\dfrac{\text{rise}}{\text{run}}$
Other ways to find the slope is to use the equation given to us.
Generally the equation of line in standard form is given as $ax+bx+c=0$ .
We can convert this equation to slope intercept from given as –
$y=mx+c$ .
Where ‘m’ is a slope, ‘c’ is the y-intercept .
So, we can find slope and intercept from here.
Now we have $x=-7$
We will convert it into the slope intercept term.
We will use an algebraic tool, we can see that we have $x=-7$ there is no y component.
So, we can write it as $x+0y=-7$ .So, our slope intercept term is $0y=-x-7$ .

As division of any term by 0 is not defined so here we cannot define the slope . So slope of $x=-7$ is undefined.

Note: Another way which is too direct to find slope is as we know standard form of line is given as $ax+by+c=0$ then we know slope is given as $\dfrac{-a}{b}$
Where ‘a’ is coefficient of ‘x’ and ‘b’ is coefficient of ‘y’.
In our equation we have $x=-7$ so changing to standard we get $1x+0y+7=0$ .
So, we have $a=1,b=0,c=7$ .
Now as slope is $m=\dfrac{-a}{b}$ , so using above value we get –
$m=\dfrac{-1}{0}$ , as divided by 0 is not defined.
So, the slope of $x=-7$ is undefined.