Which point is on the line described by the equation below?

4x−3y=−4

Answer:

[tex]D)\ -1,0[/tex]

Step-by-step explanation:

Given

[tex]4x - 3y= -4[/tex]

Required

Determine which of the options is on the line

The question requires options.

However, I'll answer using the following:

[tex]A) -3, 4[/tex]

[tex]B) -4,3[/tex]

[tex]C)\ 3, 4[/tex]

[tex]D)\ -1,0[/tex]

A point is always of the form (x,y).

So, we have to substitute values for x and y in the given equation

Considering option A:

[tex](x,y)= (-3,4)[/tex]

Substitute [tex]-3\ for\ x\ and\ 4\ for\ y[/tex] in [tex]4x - 3y= -4[/tex]

[tex]4(-3) -3(4) = -4[/tex]

[tex]-12 -12 = -4[/tex]

[tex]-24 \neq -4[/tex]

The above represents an inequality.

Hence, -3,4 does not lie on the equation

Considering option B:

[tex](x,y) = (-4,3)[/tex]

Substitute [tex]-4\ for\ x\ and\ 3\ for\ y[/tex] in [tex]4x - 3y= -4[/tex]

[tex]4(-4) - 3(3) = -4[/tex]

[tex]-16 - 9 = -4[/tex]

[tex]-25 \neq -4[/tex]

The above represents an inequality.

Hence, -4,3 does not lie on the equation

Considering option C:

[tex](x,y) = (3,4)[/tex]

Substitute [tex]3\ for\ x\ and\ 4\ for[/tex] y in [tex]4x - 3y= -4[/tex]

[tex]4(3) - 3(4) = 4[/tex]

[tex]12 - 12 = 4[/tex]

[tex]0 \neq 4[/tex]

The above represents an inequality.

Hence, 3,4 does not lie on the equation

Considering Option D:

[tex](x,y) = (-1,0)[/tex]

Substitute [tex]-1\ for\ x\ and\ 0\ for[/tex] y in [tex]4x - 3y= -4[/tex]

[tex]4(-1) - 3(0) = -4[/tex]

[tex]-4 - 0 = -4[/tex]

[tex]-4 = -4[/tex]

The above represents an equality.

So, -1,0 lies on the equation

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