Step-by-step explanation:
Hey there!!!
Here,
Given, A line passes through point (2,-2) and is perpendicular to the y= 5x+2.
The equation of a straight line passing through point is,
[tex](y - y1) = m1(x - x1)[/tex]
Now, put all values.
[tex](y + 2) = m1(x - 2)[/tex]
It is the 1st equation.
Another equation is;
y = 5x +2........(2nd equation).
Now, Comparing it with y = mx + c, we get;
m2=5
As per the condition of perpendicular lines,
m1×m2= -1
m1 × 5 = -1
Therefore, m2= -1/5.
Keeping the value of m1 in 1st equation.
[tex](y + 2) = \frac{ - 1}{5} (x - 2)[/tex]
Simplify them.
[tex]5(y + 2) = - x + 2[/tex]
[tex]5y + 10 = - x + 2[/tex]
[tex]x + 5y + 8 = 0[/tex]
Therefore the required equation is x+5y+8= 0.
Hope it helps...
