Respuesta :

Answer with explanation:

If the graph passes through two points (a,b) and (c,d) then the equation of line is:

         [tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

1)

If the graph passes through (1,0) and (0,-4)

Then the equation of line is:

       [tex]y-0=\dfrac{-4-0}{0-1}\times (x-1)\\\\\\y=\dfrac{-4}{-1}\times (x-1)\\\\\\i.e.\\\\\\y=4(x-1)\\\\\\y=4x-4[/tex]

2)

If the graph passes through (-2,0) and (0,2)

The equation of line is:

        [tex]y-0=\dfrac{2-0}{0-(-2)}\times (x-(-2))\\\\\\i.e.\\\\\\\\y=\dfrac{2}{2}\times (x+2)\\\\\\i.e.\\\\\\y=x+2[/tex]

3)

If the graph passes through (-2,0) and (0,-4)

The equation of line is:

           [tex]y-0=\dfrac{-4-0}{0-(-2)}\times (x-(-2))\\\\i.e.\\\\y=\dfrac{-4}{2}\times (x+2)\\\\\\i.e.\\\\\\y=-2(x+2)\\\\\\i.e.\\\\\\y=-2x-4[/tex]

4)

If the graph passes through (2,0) and (0,2)

The equation of line is:

[tex]y-0=\dfrac{2-0}{0-2}\times (x-2)\\\\\\i.e.\\\\\\y=\dfrac{-2}{2}\times (x-2)\\\\\\i.e.\\\\\\y=-(x-2)\\\\\\i.e.\\\\\\y=-x+2[/tex]

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The equation of a line of each graph is given below and this can be determined by using the two-point form of a line.

Simplify all the options in order to determine the equation of the line.

A)

Given :

Points  --  (-2,0) and (0,-4)

The equation of a line passing through the points (-2,0) and (0,-4) is given below:

[tex]\dfrac{y -0}{x+2}=\dfrac{-4-0}{0+2}[/tex]

y = -2(x + 2)

y = -2x - 4

B)

Given :

Points  --  (2,0) and (0,2)

The equation of a line passing through the points (2,0) and (0,2) is given below:

[tex]\dfrac{y -0}{x-2}=\dfrac{2-0}{0-2}[/tex]

y = -1(x - 2)

y = - x + 4

C)

Given :

Points  --  (1,0) and (0,-4)

The equation of a line passing through the points (1,0) and (0,-4) is given below:

[tex]\dfrac{y -0}{x-1}=\dfrac{-4-0}{0-1}[/tex]

y = 4(x - 1)

y = 4x - 4

D)

Given :

Points  --  (-2,0) and (0,2)

The equation of a line passing through the points (-2,0) and (0,2) is given below:

[tex]\dfrac{y -0}{x+2}=\dfrac{2-0}{0+2}[/tex]

y = 1(x + 2)

y = x + 2

For more information, refer to the link given below:

https://brainly.com/question/2564656

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