Question

Write the standard form of the line that passes through the given points. ( 1 , 5 ) and ( − 2 , 3 )

Answer 1

2x - 3y = - 13

Explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

The first step is to obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (- 2, 3 )

substitute these values into the formula for m

m =
`(3-5)/(-2-1)` =
`(-2)/(-3)` =
`(2)/(3)` , then

y =
`(2)/(3)` x + c ← is the partial equation

to find c , substitute either of the 2 points into the partial equation

using (1, 5 ) for x and y in the partial equation

5 =
`(2)/(3)` (1) + c =
`(2)/(3)` + c ( subtract
`(2)/(3)` from both sides )

`(15)/(3)` -
`(2)/(3)` = c , that is

c =
`(13)/(3)`

y =
`(2)/(3)` x +
`(13)/(3)` ← equation in slope- intercept form

multiply through by 3 to clear the fractions

3y = 2x + 13 ( subtract 2x from both sides )

- 2x + 3y = 13 ( multiply through by - 1 )

2x - 3y = - 13 ← equation in standard form