Answer:
A. 8x - 9y = -23
Step-by-step explanation:
(-4,-1) and (1/2,3)
We write the equation in slope intercept form y=mx+b
then we convert it into standard form
m is the slope and b is the y intercept
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]
(-4,-1) and (1/2,3)
[tex]slope = \frac{3-(-1)}{\frac{1}{2}-(-4)}[/tex]
[tex]slope = \frac{4}{\frac{1}{2}+4}[/tex]
[tex]slope = \frac{4}{\frac{9}{2}}[/tex]
[tex]slope = 4*\frac{2}{9}[/tex]
[tex]slope m =\frac{8}{9}[/tex]
To find out b we plug in (-4,-1) and slope m value in y = mx+b
-1 = (8/9) (-4) + b
[tex]-1 = -\frac{32}{9} +b[/tex]
Add 32/9 on both sides
[tex]-1+\frac{32}{9} = b[/tex]
Take common denominator 9
[tex]\frac{-9+32}{9} = b[/tex]
[tex]\frac{23}{9} = b[/tex]
So equation y = mx + b becomes
[tex]y= \frac{8x}{9} + \frac{23}{9}[/tex]
Standard form is Ax + By = C
To get standard form , multiply the whole equation by 9
9y = 8x + 23
Subtract 8x on both sides
-8x + 9y = 23
Multiply the whole equation by -1
8x - 9y = -23
