Question

How do you write the equation of the line passing through the points (3,4) and (1,-6)?

Answer 1

`y = 5x - 11`

Explanation:

There are several methods to choose from:

Method 1. Use the given points to find the gradient, then substitute one of the points as (x,y) as well as the slope (m), into `y = mx+c` to find the value of `c`.
Then substitute the values of m and c to find the final equation.

Method 2. Make simultaneous equations using each point as an (x,y) but with m and c as the unknowns. Solve for m and c and substitute them into `y = mx + c`

Method 3. There is a neat formula for exactly this case. "Find the equation if you are given two points". Quick and easy!

`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1) " for " (3,4) and (1,-6)`

`(y-(-6))/(x-1) = (4-(-6))/(3-1) = 10/2 = 5/1`

`(y+6)/(x-1) = 5/1" cross multiply and re-arrange"`

`y + 6 =5x - 5`

`y = 5x - 5-6`
`y = 5x - 11`