Answer :
Let's determine the slope and the unit rate for each table.
### Table 1: Gas Mileage
We have the following values for the number of gallons and the corresponding distances:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Gallons} & \text{Distance (mi)} \\ \hline 3 & 114 \\ \hline 6 & 228 \\ \hline 9 & 342 \\ \hline 12 & 456 \\ \hline \end{array} \][/tex]
To determine the slope (or rate of change), we can use two points from the table. Let's use the points (3, 114) and (6, 228). The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the values we have:
[tex]\[ m = \frac{228 - 114}{6 - 3} = \frac{114}{3} = 38 \][/tex]
So, the slope is 38, which means the car travels 38 miles per gallon.
Since the relationship between the number of gallons and distance is linear, this slope is also the unit rate. Hence, the unit rate is 38 miles per gallon.
### Table 2: Money Earned
We have the following values for the time and earnings:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time (h)} & \text{Earnings (\$)} \\ \hline 2 & 28 \\ \hline 4 & 56 \\ \hline 6 & 84 \\ \hline 8 & 112 \\ \hline \end{array} \][/tex]
To determine the slope, we use two points from the table. Let's use the points (2, 28) and (4, 56):
[tex]\[ m = \frac{56 - 28}{4 - 2} = \frac{28}{2} = 14 \][/tex]
So, the slope is 14, which means the earnings are \$14 per hour.
Since the relationship between time and earnings is also linear, this slope is the unit rate. Therefore, the unit rate is 14 dollars per hour.
### Summary
Gas Mileage:
- The slope is 38 miles per gallon.
- The unit rate is 38 miles per gallon.
Money Earned:
- The slope is 14 dollars per hour.
- The unit rate is 14 dollars per hour.
We have now determined the slopes and unit rates for both tables.
### Table 1: Gas Mileage
We have the following values for the number of gallons and the corresponding distances:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Gallons} & \text{Distance (mi)} \\ \hline 3 & 114 \\ \hline 6 & 228 \\ \hline 9 & 342 \\ \hline 12 & 456 \\ \hline \end{array} \][/tex]
To determine the slope (or rate of change), we can use two points from the table. Let's use the points (3, 114) and (6, 228). The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the values we have:
[tex]\[ m = \frac{228 - 114}{6 - 3} = \frac{114}{3} = 38 \][/tex]
So, the slope is 38, which means the car travels 38 miles per gallon.
Since the relationship between the number of gallons and distance is linear, this slope is also the unit rate. Hence, the unit rate is 38 miles per gallon.
### Table 2: Money Earned
We have the following values for the time and earnings:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time (h)} & \text{Earnings (\$)} \\ \hline 2 & 28 \\ \hline 4 & 56 \\ \hline 6 & 84 \\ \hline 8 & 112 \\ \hline \end{array} \][/tex]
To determine the slope, we use two points from the table. Let's use the points (2, 28) and (4, 56):
[tex]\[ m = \frac{56 - 28}{4 - 2} = \frac{28}{2} = 14 \][/tex]
So, the slope is 14, which means the earnings are \$14 per hour.
Since the relationship between time and earnings is also linear, this slope is the unit rate. Therefore, the unit rate is 14 dollars per hour.
### Summary
Gas Mileage:
- The slope is 38 miles per gallon.
- The unit rate is 38 miles per gallon.
Money Earned:
- The slope is 14 dollars per hour.
- The unit rate is 14 dollars per hour.
We have now determined the slopes and unit rates for both tables.
