Question

find the equation of a line passing through points (0,6) (5,2)

Answer 1

We know the formula \(m = \frac {y_2 - y_1} {x_2 - x_1}\). In order to get the form \(y = mx + b\), we need \(m\), and we have the points. OK, so let's plug those points in:
$$(x_1, y_1) = (0, 6) \\ (x_2, y_2) = (5, 2) \\ m = \frac {2 - 6} {5 - 0} = -\frac 4 5$$

Answer 2

Okay, now we know that, because we have two points, they obviously have x-values that satisfy this line equation. We can plug in the \(x, y\) from one point to the equation, and our new-found \(m\), to solve for \(b\), if it exists. Let's choose the point \((0, 6)\), because it is simple.
$$y = mx + b \\ x = 0; y = 6 \\ 6 = -\frac 4 5 (0) + b \\ 6 = b$$
We found \(b\). Cool. Let's now write our full equation:

Answer 3

\(y = mx + b \\ y = -\frac 4 5 x + 6\)