Question

How do you write the equation in point-slope form of the line passing through (4, 0) and (2, 6)?

Answer 1

The Answer is : `=> y - 6 = -3(x - 2)` OR `y - 0 = -3(x - 4)`

The equation is of the form:

`y - y_0 = m(x - x_0)`

where `m` is the gradient and `(x_0, y_0)` is any point that lies on the line. So either of the points `(4, 0)` or `(2, 6)`

Step 1: Find the gradient, m

`m = (6 - 0)/(2 - 4) = -3`

Step 2: Write down the equation

`=> y - 6 = -3(x - 2)` taking `(2,6)`

or `y - 0 = -3(x - 4)` taking `(4,0)`

Note that Both equations are correct as they all boil down to : `y = -3x +12` {This is the slope-intercept form}