Question

What is the equation of the line passing through the points `(4/5, 1/5)` and `(1/2, 3/2)`?

Answer 1

`y=-4.33x+3.665`

Explanation:

Since `y=mx+c`, m being the gradient and c being the intercept, we have to format the equation like this.

The calculations will be easier if we convert this into decimals, so we'll do just that:
`4/5=0.8`

`1/5=0.2`

`1/2=0.5`

`3/2=1.5`

From then on, we'll calculate the gradient using the equation:

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

`=(1.5-0.2)/(0.5-0.8)`

Notice how I put a set of coordinates to one side and another set of coordinates to another. This should give you:

`1.3/-0.3`

`=-4.33`

Now, we substitute this into the equation `y=mx+c` to get:

`y=-4.33x+c`

From here, its all a matter of substituting things in. You input a y value from one of your set of coordinates and the corresponding x value like so:

`1.5 = -4.33(0.5)+c`

So, in order to get c, you need to 'transfer' the gradient and the x value to the left hand side and 'eliminate' those variables from the right hand side:

`1.5 + 4.33(0.5)= -4.33(0.5)+c+4.33(0.5)`

#1.5 + 4.33(0.5) = c

`c=3.665`

So now, the equation you get is:

`y=-4.33x+3.665`

You can check if these values are correct by substituting the letters for your other set of coordinates.

Hope this helps!