Question

part b: which statement can be represented by the slope and y-intercept?
a. marcus has $12 in his cashapp and adds $4 per week
b. tasha bought 12 shirts and then returned 4 shirts to the store
c. gerald had $12 in his cashapp and bought a $4 snack each day
d. veronica wants to make 12 pies. she uses 4 cups of flour for each pie.

Explanation:

To determine which statement represents a linear relationship with slope and y - intercept, we analyze each option:

• Option a: Marcus has $12 (y - intercept) and adds $4 per week (slope, positive rate of change). This is a linear relationship \( y = 4x+12 \), where \( x \) is the number of weeks.
• Option b: Tasha's situation is about the number of shirts, not a relationship with a slope (rate of change) and y - intercept in the context of a linear equation with a slope - intercept form. It's just a change in the number of shirts, not a linear relationship with a slope (rate) and an initial value (y - intercept) in the way we need.
• Option c: Gerald has $12 and spends $4 per day. This is a linear relationship \( y=12 - 4x\) (negative slope), but the question is about a statement that can be represented by slope and y - intercept (the form \(y = mx + b\), and option a has a positive slope which is also a valid linear relationship. However, we need to check the context. Wait, actually, option a is a situation where the amount of money in CashApp is increasing by $4 per week with an initial $12, which is a linear function with slope 4 and y - intercept 12. Option c is a decreasing function, but both are linear. But let's re - evaluate:
• Option d: Veronica's situation is about the number of pies and cups of flour per pie. It's a relationship between the number of pies and total flour, \(y = 4x\) (if \(x\) is the number of pies), but there is no y - intercept of 12.

So, option a has an initial value (y - intercept) of 12 and a rate of change (slope) of 4, which can be represented in the slope - intercept form of a linear equation \(y=mx + b\) where \(m = 4\) (slope) and \(b = 12\) (y - intercept).

Answer:

a. Marcus has $12 in his CashApp and adds $4 per week