Question

How do you write the standard form of a line given (10,4) and (3,1)?

Answer 1

`3x-7y-2=0`

Explanation:

We are given that `"A"(10,4)` and `"B"(3,1)` lie on the line `l`. Given these two points, we can work out the gradient of the line using this formula:

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

`m_l=(1-4)/(3-10)=(-3)/-7=3/7`

We can know work out the equation of the line using this formula:

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

`y-4=3/7(x-10)`

`y-4=3/7x-30/7`

`y=3/7x-2/7`

`7y=3x-2`

Now to get it into standard form, we need to bring all the variables and constants to one side.

`3x-7y-2=0`