Question

What is the slope and y-intercept of the line $x = - 5$ ?

Answer 1

Hint : We know the equation of a line passing through a point and having a slope ‘m’ and with ‘y’ intercept as ‘c’ is given by $y = mx + c$ . Here, (x, y) is a variable. We convert the given equation to the slope intercept form. Then comparing the simplified equation with the equation of slope intercept we will get the desired result.

Complete step-by-step answer :
In the given problem, we are required to find the slope and intercept of the line whose equation is given to us as $x = - 5$ .
The slope intercept form of the equation of a line is $y = mx + c$ where slope of line is given by ‘m’ and y-intercept is given by ‘c’.
So, first we write the equation with the coefficient of y term being zero.
We get, $1x + 0y = - 5$
Shifting term consisting x to the right side of the equation,
$\Rightarrow 0y = - x - 5$
Isolating y so as to convert the equation of line to slope and intercept form, we get,
$\Rightarrow y = \dfrac{{\left( { - x - 5} \right)}}{0}$
Now, we can directly start comparing the equation of the given line with the slope and intercept form of a line and get the values of slope and intercept of the line.
Therefore, On comparing the equation of the line $y = \left( { - \dfrac{1}{0}x - \dfrac{5}{0}} \right)$ given to us and the slope intercept form of the line $y = mx + c$ , we get,
Slope of the line $= m = - \dfrac{1}{0}$ . hence, the slope of the line is undefined since division by zero is undefined.
Also, y-intercept $= c = - \dfrac{5}{0}$ . Hence, the y-intercept is also undefined.
We know that the line such as the one given in the question itself is parallel to y-axis. So, the slope of such lines is undefined. Also, the line being parallel to the y-axis does not meet the y-axis at any point. So, the y intercept is also undefined.

Note : ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph. In other words the value of ‘y’ at ‘x’ is equal to zero. Hence, the y intercept of a line can also be found by putting the value of x as zero. Slope of a line is the inclination of the straight line with positive x-axis.