Final answer:
To find the equation of the line with slope m = -5 passing through the point (-2, 6), plug these values into the slope-intercept formula y = mx + b. After solving for b, the equation of the line is y = -5x - 4.
Step-by-step explanation:
To write an equation of the line that has the slope m = -5 and contains the point (-2, 6), you use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. First, plug the slope m and the coordinates of the given point (-2, 6) into the equation to find the y-intercept b. The equation becomes:
6 = (-5)(-2) + b
Solve for b:
6 = 10 + b
b = 6 - 10
b = -4
Thus, the equation of the line is y = -5x - 4.