Question

Which is an equation of the given line in standard form?

A.
–8x + 9y = 23

B.
–8x + 9y = –23

C.
–8x + 7y = 25

D.
–9x + 8y = –23

Answer 1

-8x+9y=23 -- y=8/9x+23/9

(-4,-1), (1/2,3)
(3--1)/(1/2--4)= 4/(4 1/2)=.888888889

So answer A because if you rearrange it in y=mx+b form you see it's y=8/9x+23/9. And using the two points provided you can subtract to find the slope which comes out to be 8/9 the only two answers with that are A and B, so eliminate C and D. Then you can easily tell by looking at the graph that the y-intercept is positive, thus answer A is the only answer that works.

Answer 2

Answer : The correct option is, (A) -8x + 9y = 23

Step-by-step explanation :

The general form for the formation of a linear equation is:

`(y-y_1)=m* (x-x_1)` .............(1)

where,

x and y are the coordinates of x-axis and y-axis respectively.

m is slope of line.

First we have to calculate the slope of line.

Formula used :

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

Here,

`(x_1,y_1)=(-4,-1)` and
`(x_2,y_2)=((1)/(2),3)`

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

`m=(8)/(9)`

Now put the value of slope in equation 1, we get the linear equation.

`(y-y_1)=m* (x-x_1)`

`(y-(-1))=(8)/(9)* (x-(-4))`

`(y+1)=(8)/(9)* (x+4)`

`9* (y+1)=8* (x+4)`

`9y+9=8x+32`

`9y=8x+32-9`

`9y=8x+23`

`9y-8x=23`

From the given options we conclude that the option A is an equation of the given line in standard form.

Hence, the correct option is, (A) -8x + 9y = 23