Question

The equation of the line passing through (1, 2) and perpendicular to x+y+1=0 is ​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that l be the required equation of line which passes through the point (1, 2) and perpendicular to the line x + y + 1 = 0

Let assume that slope of line l be m

Now, Consider Equation of line x + y + 1 = 0

can be rewritten as

y = - x - 1

So, on comparing with y = mx + c, we get

Slope of line, x + y + 1 = 0 is - 1.

Given that,

Line l is perpendicular to x + y + 1 = 0

We know that,

Two lines having slope m and M are perpendicular, iff Mm = - 1

So, using this, we get

$\rm \: m \times ( - 1) = - 1$

$\rm\implies \:m = 1$

Now, We know

Point slope form of a line :- Equation of line which passes through the point (a, b) having slope m is y - b = m(x - a).

So, equation of line l which passes through the point (1, 2) and having slope m = 1 is

$\rm \: y - 2 = 1(x - 1)$

$\rm \: y - 2 = x - 1$

$\rm \: x - y - 1 + 2 = 0$

$\rm\implies \:\rm \: x - y + 1 = 0$

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ADDITIONAL INFORMATION

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to x - axis passes through the point (a, b) is x = a.

2. Point-slope form equation of line

Equation of line passing through the point (a, b) having slope m is y - b = m(x - a)

3. Slope-intercept form equation of line

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

4. Intercept Form of Line

Equation of line which makes an intercept of a and b units on x - axis and y - axis respectively is x/a + y/b = 1.

5. Normal form of Line

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle β with the positive X-axis is x cosβ + y sinβ = p.

Answer 2

Refer the given attachments