Final answer:
The equation of the line that passes through the point (-2, 10) with a slope of -4 is y = -4x + 2.
Step-by-step explanation:
The equation of a line that passes through a specific point and has a given slope can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes and m is the slope of the line. For a line that passes through the point (-2, 10) with a slope of -4, the equation can be written as:
y - 10 = -4(x - (-2)).
Simplifying this, we get:
y - 10 = -4x - 8
Adding 10 to both sides to get y by itself, we find the equation in slope-intercept form:
y = -4x + 2.
This is the linear equation of the line with the given characteristics.