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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:
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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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