Question

Find the equation of line with slope
is -4/5 and passing through the
point (2.5)​

Answer 1

EXPLANATION.

Equation of line,

Slope of the line = -4/5.

Passing through a point = (2,5).

As we know that,

Slope = m = -4/5.

⇒ x = 2.  and  y = 5.

Equation of line.

⇒ (y - y₁) = m(x - x₁).

Put the values in the equation, we get.

⇒ (y - 5) = -4/5(x - 2).

⇒ 5(y - 5) = -4(x - 2).

⇒ 5y - 25 = - 4x + 8.

⇒ 5y + 4x = 25 + 8.

⇒ 5y + 4x = 33.

                                                                                                                         

MORE INFORMATION.

Different forms of the equation of straight line.

(1) = Slope - intercept form : y = mx + c.

(2) = Slope point form : the equation of a line with slope m and passing through a point (x₁, y₁) is : y - y₁ = m(x - x₁).

(3) = Two point form : y - y₁ = y₂ - y₁/x₂ - x₁ (x - x₁).

(4) = Intercept form : x/a + y/b = 1.

(5) = Normal (perpendicular) form of a line :

x cosα + y sinα = p.

(6) = Parametric form (distance form) : x - x₁/cos∅ = y - y₁/sin∅ = r.

Answer 2

$\sf{Given, \: the \: equation \: of \: straight \: line \: passes}$

$\sf{through (−1,2) \:  and \: having \: slope \: as} \: \frac{2}{5}$

$\sf{So, \: the \: equation \: of \: the \: line \: will \: be}$

$\sf \pink{y−y1=m(x−x1)}$

$\sf \pink{Here, (x1,y1) is (−1,2)}$

$\sf{⇒y−2=( \frac{2}{5})[x−(−1)]}$

$\sf{5(y−2)=2(x+1)}$

$\sf{5y−10=2x+2}$

$\sf \pink{Thus, \: the \: line \: equation \: is  \: 2x−5y+12=0.}$