Question

1. your friend brian looks at this problem and says you dont have to bother graphing this, theres no solution. john and brenda both save 20% of their income each month, which means their lines will have the same slope. if you graph them, theyll be parallel. is brian correct? why or why not?

Explanation:

Brian is correct. In a savings - related linear equation of the form \(y = mx + b\) (where \(y\) is the total savings, \(x\) is the number of months, \(m\) is the slope, and \(b\) is the initial amount), the slope \(m\) represents the amount saved per month. If both John and Brenda save 20% of their income each month, the rate at which their savings grow (the slope) is the same. In the context of linear equations, if two lines have the same slope (\(m_1=m_2\)) and different \(y\) - intercepts (assuming their initial savings or incomes are different, so \(b_1
eq b_2\)), the lines are parallel. Parallel lines do not intersect, which means there is no solution (no point \((x,y)\) that satisfies both equations simultaneously) when we are looking for a common savings amount at the same number of months (assuming we are comparing their savings over time).

Answer:

Brian is correct. Since the slope (savings rate) is the same for both John and Brenda's savings equations and assuming their initial conditions (y - intercepts) are different, their savings lines are parallel and have no solution (no intersection point).