Question

determine the standard form of the equation of the line that passes through (6,0) and (2,-7). (-7x-4y=-42) (7x-4y=42) (-7x+4y=42) (4x+7y=-42)​

Answer 1

`7x - 4y = 42`

Explanation:

Given

`(x_1,y_1) = (6,0)`

`(x_2,y_2) = (2,-7)`

Required

Determine the equation in standard form

First, calculate the slope (m) using:

`m = (y_2 -y_1)/(x_2 - x_1)`

This gives:

`m = (-7 -0)/(2 - 6)`

`m = (-7)/(-4)`

`m = (7)/(4)`

The equation in standard form is calculated using:

`y - y_1 = m(x - x_1 )`

This gives:

`y - 0 = (7)/(4)(x - 6)`

`y = (7)/(4)(x - 6)`

Cross Multiply

`4y = 7(x - 6)`

Open bracket

`4y = 7x - 42`

Subtract 7x from both sides

`-7x + 4y = 7x - 7x - 42`

`-7x + 4y = - 42`

Multiply through by -1

`-1(-7x + 4y) = - 42*-1`

`7x - 4y = 42`