Question

Find the equation in standard form of the line passing through the points (2 -3) and (4 2)

Answer 1

5x - 2y = 16

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

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

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, 2 )

m =
`(2-(-3))/(4-2)` =
`(2+3)/(2)` =
`(5)/(2)` , then

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

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

using (4, 2 )

2 =
`(5)/(2)` (4) + c = 10 + c ( subtract 10 from both sides )

- 8 = c

y =
`(5)/(2)` x - 8 ← equation in slope- intercept form

multiply through by 2 to clear the fraction

2y = 5x - 16 ( subtract 5x from both sides )

- 5x + 2y = - 16 ( multiply through by - 1 )

5x - 2y = 16 ← equation in standard form