Question

I'm supposed to sort the larger unit rate and smaller unit rates.

Options:
a) y = 4/3x - 5/3
b) y = 5/4x - 3
c) y = -2x + 17/3
d) y = 7/4x - 9/4
e) y = 6/5x - 3/5
f) y = 8/5x - 7/5

Answer 1

To sort the unit rates from larger to smaller, we compare the slopes of the given linear equations and ignoring the sign, we list them from the one with the highest absolute value to the lowest.

Step-by-step explanation:

We need to identify and sort the equations based on their unit rates. The unit rate in a linear equation of the form y = mx + b is the coefficient 'm' which represents the rate of change or slope. A higher absolute value of 'm' indicates a larger unit rate. We will compare the slopes and sort them from larger to smaller.

• y = 7/4x - 9/4: Unit rate is 7/4 or 1.75
• y = 8/5x - 7/5: Unit rate is 8/5 or 1.6
• y = 4/3x - 5/3: Unit rate is 4/3 or approximately 1.333
• y = 5/4x - 3: Unit rate is 5/4 or 1.25
• y = 6/5x - 3/5: Unit rate is 6/5 or 1.2
• y = -2x + 17/3: Unit rate is -2 (although this is a negative rate, it is larger in magnitude than some of the positive rates)

Putting them in order from largest to smallest unit rate (ignoring the negative), we get:

1. y = 7/4x - 9/4
2. y = 8/5x - 7/5
3. y = 4/3x - 5/3
4. y = 5/4x - 3
5. y = 6/5x - 3/5
6. y = -2x + 17/3