Question

Write an equation for the line that is

perpendicular to the line y = 4x + 9
and goes through the point (2, 8).

Answer 1

`\sf y =(-1)/(4)x+(17)/(2)`

Explanation:

Equation of the line: y =mx + b

where m is slope and b is y-intercept.

y = 4x + 9

Slope = m₁ = 4

`\sf \text{Slope of the perpendicular line = $(-1)/(m_1)$}`

`\sf \boxed{m = (-1)/(4)}`

`\sf y =(-1)/(4)x +b`

The point (2,8) passes through the line. Substitute in the above equation to find 'b'.

`\sf 8 = (-1)/(4)*2+b\\\\\\ 8 = (-1)/(2)+b\\\\`

`\sf 8+(1)/(2)=b\\\\ (16)/(2)+(1)/(2)=b\\\\ \boxed{b=(17)/(2)}`

Equation of the line:

`\sf y =(-1)/(4)x + (17)/(2)`