Final answer:
The difference between Mario's and Luigi's Plumbing flat fees is $20, which is found by subtracting Luigi's y-intercept of $30 from Mario's y-intercept of $50.
Step-by-step explanation:
The question asks for the difference between the flat fees (y-intercepts) of two plumbing companies, represented by their respective linear equations. Mario's Plumbing charges a flat fee of $50, which is the y-intercept of its cost function.
The y-intercept of Mario's Plumbing fee, represented by the function f(x) = 75x + 30, can be found by setting x = 0 and solving for y. Substituting x = 0 into the function, we get: f(0) = 75(0) + 30 = 30. Therefore, the y-intercept, or flat fee, for Mario's Plumbing is $30.
For Luigi's Plumbing, the flat fee is given as $50. The difference in the companies' flat fees is calculated by subtracting the flat fee of Luigi's Plumbing from the flat fee of Mario's Plumbing: $30 - $50 = -$20.
Therefore, the difference in the companies' flat fees (y-intercepts) is -$20, which means that Luigi's Plumbing charges $20 more as a flat fee compared to Mario's Plumbing.
Luigi's Plumbing charges a flat fee given as part of its function f(x) = 75x + 30, where $30 is the y-intercept. To find the difference in flat fees, one must subtract Luigi's flat fee from Mario's:
$50 (Mario's flat fee) - $30 (Luigi's flat fee) = $20.
Therefore, the difference in their flat fees is $20, which corresponds to answer option B.