Question

Write an equation in standard form

Answer 1

3x - y = 2

Explanation:

the equation of a line in standard form is

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

obtain the equation first in slope- intercept form

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 ) = (- 1, - 5 ) and (x₂, y₂ ) = (3, 7 )

m =
`(7-(-5))/(3-(-1))` =
`(7+5)/(3+1)` =
`(12)/(4)` = 3 , then

y = 3x + c ← is the partial equation

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

using (3, 7 ) , then

7 = 9 + c ⇒ c = 7 - 9 = - 2

y = 3x - 2 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 2 ( add 2 to both sides )

2 = 3x - y , that is

3x - y = 2 ← in standard form