Final answer:
The equation of the line in slope-intercept form is y = 9x - 5.
Step-by-step explanation:
To determine the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
The formula for slope is: m = (y2 - y1) / (x2 - x1)
Using the given points (-1, -14) and (2, 13), we can substitute the coordinates into the formula:
m = (13 - (-14)) / (2 - (-1))
Simplifying gives us m = 27 / 3 = 9
The y-intercept (b) can be found by substituting one of the given points into the equation y = mx + b.
Using point (-1, -14), -14 = 9(-1) + b
Solving for b, we get b = -5
Therefore, the equation of the line is: y = 9x - 5