Question

Write the equation of the line that is perpendicular to y = 2/5x- 7 that passes through

the point (8, -3).

Answer 1

`y=-(5)/(2)x+17`

Explanation:

Equation of the Line

The general equation of a line of slope m and y-intercept b can be expressed as:

`y=mx+b`

The given equation is:

`\displaystyle y=(2)/(5)x-7`

Its slope is m1=2/5. The required line is perpendicular to the other and let's assume its slope is m2. Two lines are perpendicular if their slopes comply with the relationship:

`m_1m_2=-1`

The second slope can be calculated as:

`\displaystyle m_2=-(1)/(m_1)`

`\displaystyle m_2=-(1)/(2/5)=-(5)/(2)`

The equation of the required line is:

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

To find the value of b, we use the point (8,-3):

`-3=-(5)/(2)(8)+b`

`-3=-20+b`

Solving for b:

b=17

The equation of the line is

`\boxed{y=-(5)/(2)x+17}`