Final answer:
The equation of the line in slope-intercept form that passes through the points (-6, 14) and (5, -41) is y = -5x -16.
Step-by-step explanation:
To write an equation in slope-intercept form of a line that passes through the points (-6, 14) and (5, -41), we need to find the slope (m) and the y-intercept (b).
The formula to find the slope is:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m = (-41 - 14) / (5 - (-6))
m = (-55)/(11) = -5
Now, we can use one of the given points and the slope to find the y-intercept:
y = mx + b
Using (-6, 14), we get:
14 = -5(-6) + b
14 = 30 + b
b = 14 - 30
b = -16
Therefore, the equation of the line in slope-intercept form is:
y = -5x -16