x/y

Question

(−5)(0)
(0)(5)
(2)(7)
Which linear equation represents this nonproportional linear relationship using the table above?
1. y = -5x + 5
2. y = -x + 5
3. y = frac(1)(5)x + 5
4. y = x + 5

Answer 1

To find the linear equation that represents the non-proportional linear relationship based on the provided coordinates, we can use the points listed in the table:

1. (-5, 0)
2. (0, 5)
3. (2, 7)

From the points, we can derive the line's equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, we can use the points (0, 5) and (2, 7) to calculate the slope:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]

Now that we have the slope \( m = 1 \) and the y-intercept \( b = 5 \) (from the point where x = 0), we can write the equation of the line:

\[ y = 1x + 5 \quad \text{or simply} \quad y = x + 5 \]

Thus, the correct answer is:

4. \( y = x + 5 \)