Question

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

Answer 1

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

Step-by-step explanation :

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

$(y-y_1)=m\times (x-x_1)$          .............(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 :

$m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Here,

$(x_1,y_1)=(-4,-1)$ and $(x_2,y_2)=(\frac{1}{2},3)$

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

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

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

$(y-y_1)=m\times (x-x_1)$

$(y-(-1))=\frac{8}{9}\times (x-(-4))$

$(y+1)=\frac{8}{9}\times (x+4)$

$9\times (y+1)=8\times (x+4)$

$9y+9=8x+32$

$9y=8x+32-9$

$9y=8x+23$

$9y-8x=23$

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

Answer 2

-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.