Question

Find the equation of straight line which passes through tge points A(5, 10) and B(-13, -14)

Answer 1

`y=(4)/(3)x+(10)/(3)`

Given:

A (5, 10)

B (-13, -14)

First, let us find the slope

`m=(y_2-y_1)/(x_2-x_1)`
`m=(-14-10)/(-13-5)`
`m=(-24)/(-18)`
`m=(4)/(3)`

Next, we will use the following formula to solve for the equation of the line

`y=mx+b`

Using the point A (5, 10), and the slope, solve for b

`10=((4)/(3))(5)+b`
`10=(20)/(3)+b`
`10-(20)/(3)=b`
`(10)/(3)=b`

Now that we have the slope m, and the value of b, substitute it to this equation to get the equation of the line

`y=mx+b`
`y=(4)/(3)x+(10)/(3)`