Question

What is the equation of the line that passes through (2, 1) and (5, -1)?

Answer 1

`y = (-2)/3x +(7)/(3)`

Explanation:

Since we have two points the first thing I would do is calculate the gradient of the line.

We can use the formula gradient(m) `=(Deltay)/(Deltax) = (y_2 - y_1) / (x_2 - x_1)`

We then need to select our values to substitute into the equation, for this we will take our first point `(2,1)` and make `x_1 = 2` and `y_1 = 1`. Now take the second point `(5 -1)` and make `x_2 = 5` and `y_2 = -1`. Simply substitute the values in the equation:

gradient(m) `=(Deltay)/(Deltax) = (y_2 - y_1) / (x_2 - x_1) = (-1 - 1) / (5 - 2) = (-2)/(3)`

Now that we have the gradient substitute that into `y = mx + c` so that `y = (-2)/3x +c`

To find `c` we need to use one of the given points, so substitute one of these points into our equation: `y = (-2)/3x +c` In this explanation we will use `(2,1)`. So `1 = (-2)/(3)(2) +c`

Now solve as a linear equation to obtain `c`:

`1 = (-4)/(3) +c`
`1 - (-4)/(3) = c`
`(7) / (3) = c`
`c = (7) / (3)`

Substitute the value for `c` into the equation: `y = (-2)/3x +c` so that `y = (-2)/3x +(7)/(3)`