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 ) = ( [tex]\frac{1}{2}[/tex], 3) and (x₂, y₂ ) = (- 4, - 1 )
m = [tex]\frac{-1-3}{-4-1/2}[/tex] = (- 4)/- [tex]\frac{9}{2}[/tex] = [tex]\frac{8}{9}[/tex]
partial equation is y = [tex]\frac{8}{9}[/tex] x + c
to find c substitute either of the 2 points into the partial equation
using (- 4, - 1 ), then
- 1 = - [tex]\frac{32}{9}[/tex] + c ⇒ c = [tex]\frac{23}{9}[/tex]
y = [tex]\frac{8}{9}[/tex] x +[tex]\frac{23}{9}[/tex] ← 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
