Question

write the equation of the line is perpendicular to the line y=-1/5x+9 and passes through the point -2 ,-2

Answer 1

Answer:

$y=5x + 8$

Step-by-step explanation:

Given line is $y=(\frac{-1}{5})x + 9$

so, the slope of the given line is $\frac{-1}{5}$.

now, let the line which is perpendicular to the given line be y = mx + c

where,

m = slope of the line

c = constant

As we know, if two lines are perpendicular to each other, the value of product of there slopes are -1.

so, slope of given line × slope of perpendicular line = -1

⇒ $(\frac{-1}{5})m=(-1)$

⇒ $m=5$

By substitutiong the value of m in the equation, we get;

⇒ $y=5x + c$

For c,

as the point (-2,-2) passes through the line, we get;

⇒ $-2=5(-2) + c$

⇒ $c=8$

Hence,

The line which is perpendicular to the given line and passes through (-2,-2) is

$y=5x + 8$