Final answer:
The equation of the line with a slope of -5 that passes through the point (1,-9) is y = -5x - 4. This line has a constant downward slope.
Step-by-step explanation:
To write the equation of a line with a slope of -5 that passes through the point (1,-9) in slope-intercept form, you start with the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, you are given that m=-5. To find b, you use the given point that the line passes through. Plug the coordinates of that point into the equation and solve for b:
y = mx + b
-9 = (-5)(1) + b
-9 = -5 + b
b = -9 + 5
b = -4
Now that you have both m, which is -5, and b, which is -4, you can write the final equation of the line in slope-intercept form:
y = -5x - 4
This equation represents a line that has a constant downward slope, meaning that for every unit increase in x, y decreases by 5 units.