Answer:
[tex]y=\dfrac{-x}{5}+2[/tex]
Step-by-step explanation:
The given equation of line :
y = 5x + 3 ....(1)
The general equation of a line is :
y = mx +b ...(2)
From equation (1) and (2)
Slope, m = 5
The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal such that,
[tex]m_1\times m_2=-1\\\\m_2=-\dfrac{1}{5}[/tex]
The perpendicular slope = -1/5. It contains point A(0,7).
Put x = 0 and y = 7 in eqution (2)
[tex]2=(\dfrac{-1}{5})(0)+b\\\\b=2[/tex]
Hence, required equation that is perpendicular to the line y = 5x + 3 is :
[tex]y=\dfrac{-x}{5}+2[/tex]
