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1. Equation of line parallel, perpendicular and point of intersection

An equation of first degree and the form

$ax + by + c = 0$ represents a straight line.

Here,

$x$ and

$y$ are variables,

$a$ ,

$b$ and

$c$ are real numbers, and either

$a \neq 0$ or

$b \neq 0$ .

Now, let us determine

(i) the equation of a straight line parallel to

$ax + by + c = 0$ .

(ii) the equation of a straight line perpendicular to

$ax + by + c = 0$ .

(iii) the point of intersection of two intersecting straight lines.

Equation of a line parallel to $ax + by + c = 0$

The equations of all lines parallel to

$ax + by + c = 0$ are of the form

$ax + by + k = 0$ , for different values of

$k$ .

Equation of a line perpendicular to $ax + by + c = 0$

The equations of all lines perpendicular to

$ax + by + c = 0$ are of the form

$bx - ay + k = 0$ , for different values of

$k$ .

The point of intersection of two intersecting straight lines

If two straight lines are not parallel, then the lines must intersect at some point. Hence, the point of intersection of these two straight lines can be determined by solving the equations.

Important!

Two straight lines

$a_1x + b_1y + c_1 = 0$ and

$a_2x + b_2y + c_2 = 0$ , where the coefficients are non-zero,

(i) are parallel if and only if

$\frac{a_1}{a_2} = \frac{b_1}{b_2}$

(ii) are perpendicular if and only if

$a_1a_2 + b_1b_2 = 0$

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1. Equation of line parallel, perpendicular and point of intersection

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