Answer :
-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.
(-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 : The correct option is, (A) -8x + 9y = 23
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(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 :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(-4,-1)[/tex] and [tex](x_2,y_2)=(\frac{1}{2},3)[/tex]
[tex]m=\frac{(3-(-1))}{(\frac{1}{2}-(-4))}[/tex]
[tex]m=\frac{8}{9}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-(-1))=\frac{8}{9}\times (x-(-4))[/tex]
[tex](y+1)=\frac{8}{9}\times (x+4)[/tex]
[tex]9\times (y+1)=8\times (x+4)[/tex]
[tex]9y+9=8x+32[/tex]
[tex]9y=8x+32-9[/tex]
[tex]9y=8x+23[/tex]
[tex]9y-8x=23[/tex]
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
