Question

9.Lucas's saving balance is represented by the line y = 40x+ 20 graphed below. Marcos's savings

balance is represented by the line y = 30x + 90 graphed below. What does the intersection of the two
lines represent?
savings (S)
600
-550
-500
-450
400+
-350
-300
-250
-200
-150
-100
50
0
-50
9
10
11 12 13 14
a. Marcos is saving $7 more than Lucas per week
b. Marcos has saved $300 more than Lucas after 7 weeks
c. They both saved $300 per week in the 7th week
d. They both have saved $300 total after 7 weeks
15
weeks

Answer 1

The intersection of Lucas and Marcos's savings balance lines represents the point at which both have saved a total of $300 after 7 weeks.

Step-by-step explanation:

The intersection of two linear equations on a graph represents the point where both equations have the same value for 'y' given the same value for 'x'.

In this context of savings balances over time, Lucas's savings balance is represented by the line y = 40x + 20, and Marcos's savings balance is represented by the line y = 30x + 90.

If we set these two equations equal to each other to find their intersection:

40x + 20 = 30x + 90

Solving for 'x', we subtract 30x from both sides:

10x + 20 = 90

Then subtract 20 from both sides:

10x = 70

And divide by 10:

x = 7

Now, we'll find the value of 'y' when x is 7.

y = 40(7) + 20 = 280 + 20 = 300

Thus, the intersection point is at (7, 300). This means that after 7 weeks, both Lucas and Marcos have saved a total of $300. The correct answer based on the choices provided is d. They both have saved $300 total after 7 weeks.