Question

Write an equation that is perpendicular to the line y = 5x + 3 that contains point A(0,7).

Answer 1

`y=(-x)/(5)+2`

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,

`m_1* m_2=-1\\\\m_2=-(1)/(5)`

The perpendicular slope = -1/5. It contains point A(0,7).

Put x = 0 and y = 7 in eqution (2)

`2=((-1)/(5))(0)+b\\\\b=2`

Hence, required equation that is perpendicular to the line y = 5x + 3 is :

`y=(-x)/(5)+2`