Question

How do you find the slope of a given equation \[x=-4\]?

Answer 1

Hint: The degree of the equation is the highest power to which the variable is raised. The degree of the equation decides if the equation is linear, quadratic, cubic, etc. The standard form of the straight-line equation is \[ax+by+c=0\]. The slope of the straight-line can be calculated using the coefficients of the equation. The slope of the straight line is \[\dfrac{-a}{b}\]. If we get the slope of a straight line as \[\infty \]. It means that the straight line is perpendicular to the Y-axis.

Complete step by step answer:
We are asked to find the slope of the equation \[x=-4\]. By adding 4 to both sides of the equation this can be also written as,
\[\begin{align}
  & \Rightarrow x+4=-4+4 \\
 & \Rightarrow x+4=0 \\
\end{align}\]
The highest power of the variable in the equation is 1, hence the degree is 1. It means that the equation is linear and it represents a straight line. The standard form of the straight-line equation is \[ax+by+c=0\]. The slope of the straight-line can be calculated using the coefficients of the equation. The slope of the straight line is \[\dfrac{-a}{b}\]. Comparing the equation with the standard form we get, \[a=1,b=0\And c=4\]. Using the formula of slope, we get the slope of the equation as,
\[\begin{align}
  & \Rightarrow slope=\dfrac{-a}{b} \\
 & \Rightarrow slope=\dfrac{-1}{0}=\infty \\
\end{align}\]
The slope of the equation is \[\infty \], it means that the straight line is perpendicular to the Y-axis.

Note:
 The relationship between the coefficients and the slope should be remembered to solve these types of problems. Along with slope, X-intercept, Y-intercept of the straight line can also be found using the coefficient of the equation.