Question

Use the information on the graph to enter an equation in standard form.?
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Answer 1

The required standard equation is
`y = 8x -8`.

we took two points to write this equation (0,-8) and (2,8).

Explanation:

Let
`(0,-8) = (x1,y1)\\(2,8) = (x2,y2)`

The equation of line passing through two point is given as

`(y - y1) = (y2-y1)/(x2-x1) * (x - x1)\\`

substituting (x1,y1) and (x2,y2) in above equation we get

`(y - -8) = (8--8)/(2-0) * (x - 0)\\`

`(y + 8) = (8+8)/(2) * (x)\\`

`(y + 8) = (16)/(2) * (x)\\`

`(y + 8) = 8* (x)\\`

`y = 8x - 8\\`

which is the required equation

Answer 2

`y-8x=-8` is the equation in standard form.

Explanation:

Lets choose two coordinate point from the graph
`(x_1,y_1) =(0,-8)`
`(x_2,y_2)=(2,8)`.

Now we will try to find out its slope from point-slope form.

Slope (m) =
`(y_2-y_1)/(x_2-x_1) =(8-(-8))/(2-0)=(16)/(2) = 8`

No we will use
`y-y_1 =m(x-x_1)`

So
`y-8=8(x-2)\ , y-8=16x-16\ , y=16x-16+8`

Now this can be arranged in Ax+By=C form that is the standard form of a line.

Re-arranging the values.

We have
`y-8x=-8` as our equation in standard form.