Let's look at an example that I think might be helpful:

Find the equation of the line containing the points $(0,4)$ and $(-3,10)$. Give your answer in slope-intercept form.

We want a line of the form $y=mx+b$ containing $(0,4)$ and $(-3,10)$. First we recognize $(0,4)$ as the y-intercept, so $b=4$. To find $m$, we calculate the slope between the two points: $$\frac{10-4}{-3-0} = \frac{6}{-3} = -2.$$ Therefore our line is $y = -2x+4$.