Question

Write an equation that is perpendicular to y=5x−4 and goes through the point (10, -1)

Answer 1

Answer:

Equation of the perpendicular line is $y=-\frac{1}{5}x+1$

Step-by-step explanation:

Given equation is y = 5x - 4

By comparing this equation with slope-intercept form of the equation,

y = mx + b

Slope of this line $m_{1}=5$

Let the slope of the perpendicular line = $m_{2}$

By the property of perpendicular lines,

$m_{1}\times m_{2}=(-1)$

$5\times m_{2}=(-1)$

$m_{2}=-\frac{1}{5}$

Equation of the perpendicular line passing through a point $(x_{1}, y_{1})$ and slope m is represented by

$y-y_{1}=m(x-x_{1})$

If the given point is (10, -1) and slope 'm'= $-\frac{1}{5}$

$y+1=-\frac{1}{5}(x-10)$

$y=-\frac{1}{5}x+2-1$

$y=-\frac{1}{5}x+1$