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Let's say Mom needs to earn $x each weekend.
Over 8 weekends, she would earn a total of 8 * x.
If she currently has $130, then by the end of the summer, she would have a total of 130 + 8 * x.
According to the problem, she wants at least $1250 by the end of the summer, so we can write the equation:
130 + 8 * x ≥ 1250
Subtracting 130 from both sides of the inequality, we get:
8 * x ≥ 1120
Dividing both sides of the inequality by 8, we get:
x ≥ 140
Therefore, she needs to earn at least $140 each weekend.
To graph the solution on a number line, we can plot all the possible values for x that satisfy the inequality. In this case, since x ≥ 140, we would fill in all the numbers from 140 onwards on the number line.