It can be helpful to plot the two points on a graph.
The slope of a line is the ratio of the vertical change to the horizontal change. We sometimes refer to that as "rise over run." In the figure, we have used the symbol ∆ to mean "the change in", so the equation m=∆y/∆x means the slope (m) is the change in y-value divided by the change in x-value.
Those changes can be measured anywhere on the line (since the slope of a line is the same everywhere), but it is convenient to use the given points. Here, the vertical difference between the points is 10-6 = 4; the horizontal change is 8-0 = 8. The slope is the ratio of these: 4/8 = 1/2. This is the value that is used for the coefficient of x in the equation of the line.
The y-intercept is the value of y where the line crosses the y-axis. Since you are given the point (0, 6), you know the line crosses the y-axis at y=6. This is the constant value in the equation of the line.
Filling in these numbers, you have
... slope-intercept form of y = 1/2 x + 6