Question

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

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

Answer 1

A. 8x - 9y = -23

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 = (y_2-y_1)/(x_2-x_1)`

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

`slope = (3-(-1))/((1)/(2)-(-4))`

`slope = (4)/((1)/(2)+4)`

`slope = (4)/((9)/(2))`

`slope = 4*(2)/(9)`

`slope m =(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 = -(32)/(9) +b`

Add 32/9 on both sides

`-1+(32)/(9) = b`

Take common denominator 9

`(-9+32)/(9) = b`

`(23)/(9) = b`

So equation y = mx + b becomes

`y= (8x)/(9) + (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