Ask a New Question
Menu

Use the table to answer the question

x y
-5 0
0 5
2 7

Which linear equation represents this nonproportional linear relationship?

answers:

y = x + 5

y = -5x + 5

y = 1/5x + 5

y = -x + 5

3 answers

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:

  1. (0, 5)
  2. (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:

\(y = x + 5\)

you sure

Let’s double-check the calculations to ensure everything is accurate for the data provided.

We have the points from the table:

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

Step 1: Calculate the slope (m) again

Using the points \((0, 5)\) and \((2, 7)\):

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

Using the points \((-5, 0)\) and \((0, 5)\):

\[ m = \frac{5 - 0}{0 - (-5)} = \frac{5}{5} = 1 \]

Using the points \((2, 7)\) and \((0, 5)\):

\[ m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]

The slope \(m\) is consistently \(1\) for the relationships derived from all possible pairs of points.

Step 2: Identify the y-intercept (b)

We can also look at point (0, 5) to determine the y-intercept directly, which is:

\[ b = 5 \]

Step 3: Write the linear equation

Substituting the slope \(m\) and y-intercept \(b\) into the slope-intercept form equation gives us:

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

Verification with all points

  • For \(x = -5\): \[ y = -5 + 5 = 0 \quad \text{(matches the point \((-5, 0)\))} \]
  • For \(x = 0\): \[ y = 0 + 5 = 5 \quad \text{(matches the point \((0, 5)\))} \]
  • For \(x = 2\): \[ y = 2 + 5 = 7 \quad \text{(matches the point \((2, 7)\))} \]

Conclusion

From all checks, the calculations confirm that the correct equation that represents the nonproportional linear relationship from the table is indeed:

\(y = x + 5\)

So, my original response is accurate.