Calculadora de Líneas Paralelas y Perpendiculares
Encuentra rectas paralelas y perpendiculares paso a paso
La calculadora encontrará la ecuación de la línea paralela/perpendicular a la línea dada que pasa por el punto dado, con pasos mostrados.
Para dibujar líneas, use la calculadora gráfica.
Solution
Your input: find the equation of the line perpendicular to the line $$$y=- 4 x - 1$$$ passing through the point $$$\left(-2,2\right)$$$.
The equation of the line in the slope-intercept form is $$$y=- 4 x - 1$$$.
The slope of the perpendicular line is negative inverse: $$$m=\frac{1}{4}$$$.
So, the equation of the perpendicular line is $$$y=\frac{x}{4}+a$$$.
To find $$$a$$$, we use the fact that the line should pass through the given point: $$$2=\left(\frac{1}{4}\right) \cdot \left(-2\right)+a$$$.
Thus, $$$a=\frac{5}{2}$$$.
Therefore, the equation of the line is $$$y=\frac{x}{4} + \frac{5}{2}$$$.
Answer: $$$y=\frac{x}{4} + \frac{5}{2}$$$.