Question

(2,-5); x-4y=20 write an equation through the point and perpendicular to the given line

Answer 1

y = -4x + 3

Explanation:

Product of slope of the perpendicular lines is (-1).

• Write the equation in slope y-intercept form: y =mx +b.
• Subtract 'x' from both sides.

x - 4y = 20

-4y = -x - 20

• Divide both sides by (-4)

`\sf (-4y)/(-4)=(-1)/(-4)x+(20)/(-4)\\\\\\y = (1)/(4)x - 5`

Slope of the given equation = m = 1/4

• 
  `\sf Slope \ of \ the \ line \ perpendicular \ to \ x - 4y = 20, m_1 =(-1)/(m)`

`m_1 = -1 / (1)/(4)\\\\\\~~~= -1 *4\\\\~~~ = -4`

• Equation of the line: y = -4x + b
• This line is passing through (2 ,-5)

-5 = -4*2 + b

-5 = -8 + b

-5 + 8 = b

b = 3

Equation of the perpendicular line:

y = -4x + 3