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find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y

Sagot :

Lines can be perpendicular or parallel to one another.

  • The parallel line's equation is y = mx - am + c.
  • The perpendicular line's equation is y = -(x/m) + a/m + c.

What do we mean by linear equation?

  • A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept.
  • The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.

So,

A linear equation is written as:  y = mx + b

Where, m = slope.


(A) Parallel equation:

The slope of a line parallel to y = mx + b is the same as the slope of y = mx + b, that is the slope is the equation in m.

The equation is then solved as follows:

  • y = m(x - x₁) + y₁

Where:

  • (x₁,y₁) = (a,c)

Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁ as follows:

y = m (x - a) + c

y = mx - am + c

So, the equation of a line is y = mx - am + c.

(B) Parallel equation:

The slope (m2) of a perpendicular line to y = mx + b is:

  • m₂ = -(1/m)

The equation is then solved as follows:

  • y = m₂(x - x₁) + y₁

Where:

  • (x₁,y₁) = (a,c)
  • m₂ = -(1/m)

Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁

  • y = -(1/m)(x - a) + c
  • y = -(x/m) + a/m + c

The perpendicular line's equation is y = -(x/m) + a/m + c.

Therefore, lines can be perpendicular or parallel to one another.

  • The parallel line's equation is y = mx - am + c.
  • The perpendicular line's equation is y = -(x/m) + a/m + c.

Know more about the linear equation here:

https://brainly.com/question/2030026

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The correct question is given below:
Find the equations for the lines through the point (a,

c.that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. use y for the dependent variable and all letters in lower case.

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