Question

What is the equation of this line in standard form?

A 9x-8y=23
B 8x-7y -25
C 8x 9y=-23
D 8x-9y=23

Answer 1

Ostioporosis the third on Monday with your mothers earwax

Answer 2

8x - 9y = - 23

Explanation:

the equation of a line in standard form is

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

First , find the equation 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 ) = (- 4, - 1) and (x₂, y₂ ) = (
`(1)/(2)`, 3) ← 2 points on the line

m =
`(3-(-1))/((1)/(2)-(-4) )` =
`(3+1)/((1)/(2)+4 )` =
`(4)/((9)/(2) )` = 4 ×
`(2)/(9)` =
`(8)/(9)`

then y =
`(8)/(9)` x + c ← is the partial equation

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

using (- 4, - 1 ) , then

- 1 = -
`(32)/(9)` + c ⇒ c = - 1 +
`(32)/(9)` =
`(23)/(9)`

y =
`(8)/(9)` x +
`(23)/(9)` ← equation in slope- intercept form

multiply through by 9 to clear the fractions

9y = 8x + 23 ( subtract 9x from both sides )

0 = 8x - 9y + 23 ( subtract 23 from both sides )

- 23 = 8x - 9y , that is

8x - 9y = - 23 ← in standard form