To determine the linear equation that represents the given nonproportional linear relationship, we can first identify two points from the table to find the slope and then use the slope-intercept form \(y = mx + b\).
From the table, we can select two points:
- (0, 5)
- (2, 7)
Step 1: Calculate the slope (m)
The slope \(m\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (0, 5) and (2, 7):
\[ m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]
Step 2: Use the y-intercept (b)
Since one of our points is (0, 5), we can see that when \(x = 0\), \(y = 5\). This means the y-intercept \(b\) is 5.
Step 3: Write the equation
Now we can write the equation using the slope-intercept form \(y = mx + b\):
\[ y = 1x + 5 \quad \text{or simply} \quad y = x + 5 \]
Step 4: Find the answer in the options provided
Looking at the answer options:
- \(y = x + 5\)
- \(y = -5x + 5\)
- \(y = \frac{1}{5}x + 5\)
- \(y = -x + 5\)
The correct answer that represents the nonproportional linear relationship in the table is:
\(y = x + 5\)