Final answer:
To locate two points that are 3 units away from -4 on a number line, we find the points -1 and -7 using the equation |x + 4| = 3, which covers both directions from the central point.
Step-by-step explanation:
To find the coordinates of two points on a number line that are 3 units away from the point with coordinate -4, we consider one point to be -4 + 3 and the other to be -4 - 3. This leads us to calculate the coordinates as follows:
The point to the left of -4 is -4 - 3 = -7.
The equation that gives the coordinates of both points is |x + 4| = 3, because the absolute value represents the distance from -4 on the number line, and it can be either to the right or left of -4, hence the two solutions -1 and -7.