Question

What is the equation of this line is standard form (-4,-1) and (1/2,3)

Answer 1

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

$slope = \frac{y_2-y_1}{x_2-x_1}$

(-4,-1) and (1/2,3)

$slope = \frac{3-(-1)}{\frac{1}{2}-(-4)}$

$slope = \frac{4}{\frac{1}{2}+4}$

$slope = \frac{4}{\frac{9}{2}}$

$slope = 4*\frac{2}{9}$

$slope m =\frac{8}{9}$

To find out b we plug in (-4,-1)  and slope m value in y = mx+b

-1 = (8/9) (-4) + b

$-1 = -\frac{32}{9} +b$

Add 32/9 on both sides

$-1+\frac{32}{9} = b$

Take common denominator 9

$\frac{-9+32}{9} = b$

$\frac{23}{9} = b$

So equation y = mx + b becomes

$y= \frac{8x}{9} + \frac{23}{9}$

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