How do you graph the inequality #y<=-5x-5 #?

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality. The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y+5)^2-0.075)((x+1)^2+y^2-0.075)(5x+y+5)=0 [-15, 15, -7.5, 7.55]}

Now, we can shade the left side of the line.

graph{(5x+y+5) <= 0 [-15, 15, -7.5, 7.55]}

To graph the inequality y ≤ -5x - 5, you would first graph the boundary line y = -5x - 5 as a dashed line (since the inequality is ≤, not <).

To graph the boundary line:

1. Find two points that satisfy the equation y = -5x - 5. For example, when x = 0, y = -5(0) - 5 = -5, giving you the point (0, -5).
2. Another point could be (1, -10): y = -5(1) - 5 = -10.
3. Plot these points and draw a dashed line through them.

Next, since y is less than or equal to -5x - 5, you shade the region below the boundary line. This shading represents all the points that satisfy the inequality.