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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

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 class=


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.

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

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