Question

What would the answers to these be?

Answer 1

The first equation, 8x - 9y = - 23

Obtain the equation in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (
`(1)/(2)`, 3) and (x₂, y₂ ) = (- 4, - 1 )

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

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

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

using (- 4, - 1 ), then

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

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

the equation of a line in standard form is

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

rearrange the slope- intercept equation into this form

multiply through by 9

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

8x - 9y = - 23 in standard form