The equation of a line can be written in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Let's start by finding the slope. The slope formula is m = (y2 - y1) / (x2 - x1). Using this formula, we can substitute the given points (-6, -19) and (2,5) into the formula.
We get m = (5 - (-19)) / (2 - (-6)) which results in m = 24 / 8. Thus, m = 3.
So, the slope of the line is 3.
Next, we need to find the y-intercept (b).
We can use the formula b = y1 - m*x1. Substituting x1 = -6, y1 = -19, and m = 3 into this formula, we get b = -19 - 3*(-6), which simplifies to b = -19 + 18, therefore b = -1.
Therefore, the y-intercept is -1.
Using the obtained slope and y-intercept values, we can now write the equation of the line. The equation of the line is y = 3x - 1.
So, that's our answer. The equation of the line passing through the points (-6, -19) and (2,5) is y = 3x - 1.