write the standard form of the equation of the line through the given points of (0,2) and (5,0)

Question

write the standard form of the equation of the line through the given points

Throuh: (0,2) and (5,0)

Answer 1

Given points (x1,y1) = (0,2)

(x2,y2) = (5,0)

Standard form of line equation is y-y1 = m (x-x1)

m = y2-y1/x2-x1

m =(0-2)/(5-0)

= -2/5

Eqution is y-2 = -2/5(x-0)

y-2  = -2/5x

Add 2 to each side.

y-2+2 = -2/5x+2

Required line equation is y = -2/5x+2.

Answer 2

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

 

Let the points are (x₁, y₁) = (0, 2) and (x₂, y₂) = (5, 0).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(0 - 2)/(5 - 0)]

m  = [- 2/5]

⇒ m = - 2/5.

Now, the line equation is y = (- 2/5)x + b.

 

Find the y - intercept by substituting any point in the line equation say (x, y) = (0, 2).

2 = (- 2/5)(0) + b

⇒ b = 2.

The line equation in slope - intercept - form is y = (- 2/5)x + 2.

 

Write the equation y = (- 2/5)x + 2 in standard form of line equation.

Multiply each side by 5.

5y = 5[ (- 2/5)x + 2 ]

5y = - 2x + 10

Add 2x to each side.

5y + 2x = - 2x + 10 + 2x

5y + 2x = 10.

The standard form of line equation is 2x + 5y = 10.