Question

How do you find the equation of the straight line joining: (3, -1), (5, 4)?

Answer 1

`y=(5x-17)/2`

Explanation:

Firstly, there are two different formula that can be used to answer the question:

`y = mx+c`
or
`y-y_1 = m(x-x_1)`

The first formula will take more time to work through, as you have to rearrange to find `y`, then substitute it back in. The second formula is recommended as it means you don't have to do this. However regardless of which route you take, you first have to calculate `m`, the gradient:

`m = (y_2-y_1)/(x_2-x_1)=(4-(-1))/(5-3)=5/2`

Now we have the gradient, simply choose a point and use the second formula:

`y-y_1 = m(x-x_1) -> y-4 = 5/2(x-5) ->`
`y-4 = (5x-25)/2 -> y=(5x-25+8)/2 -> y=(5x-17)/2`