Question

The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line? y = -2x + 6 y = 13x – 6 y = 3x – 2 y = 13x – 2

Answer 1

`$ 2x - 3y - 6 = 0$`

Explanation:

When we are to find the equation of the line passing through two points, say
`$ (x_1, y_1) $` and
`$ (x_2, y_2) $` we use the two -point form.

The two point form is as follows:

`$ \frac{y - y_1} {y_2 - y_1} = (x - x_1)/(x_2 - x_1) $`

Here,
`$ (x_1 , y_1) = (0 , -2) $` and
`$ (x_2, y_2) = (6 , 0) $`.

Therefore we have:
`$ (y + 2)/(0 + 2) = (x - 0)/(6 - 0) $`

`$ \implies (y + 2)/(1) = (x)/(3) $`

`$ \implies 3y + 6 = x $ $ \implies x -3y + 6 = 0$`

Answer 2

The equation of the line is
`y = (x)/(3) - 2`

Explanation:

Given

Point 1 (0, -2)

Point 2 (6, 0).

Required

What is the equation of the line?

To get the equation of the line, we have to calculate the two -point form gradient formula.

Let gradient be represented by m

The expression for m is as follows;

`m = (y - y_(1) )/(x - x_(1))` and

`m = (y_(2) - y_(1) )/(x_(2) - x_(1))`

Since m = m, we have

`(y - y_(1) )/(x - x_(1)) = (y_(2) - y_(1) )/(x_(2) - x_(1))`

Such that

`x_(1) = 0, x_(2) = 6, y_(1) = -2, y_(2) = 0`

By Substituting these values in the expression above, we'll get the equation of the line

`(y - y_(1) )/(x - x_(1)) = (y_(2) - y_(1) )/(x_(2) - x_(1))`

becomes

`(y - (-2) )/(x - 0) = (0 - (-2) )/(6 - 0)`

`(y + 2 )/(x) = (0 + 2 )/(6)`

`(y + 2 )/(x) = (2 )/(6)`

`(y + 2 )/(x) = (1)/(3)`

Multiply 3x to both sides

`3x * (y + 2 )/(x) = (1)/(3) * 3x`

`3 ( {y + 2 }) = x`

Open bracket

`3y + 6 = x`

Make y the subject of formula

`3y = x - 6`

Divide both sides by 3

`y = (x - 6)/(3)`

`y = (x)/(3) - (6)/(3)`

`y = (x)/(3) - 2`

Hence, the equation of the line is
`y = (x)/(3) - 2`