Question

Use the table to answer the question. x y −5 0 0 5 2 7 Which linear equation represents this nonproportional linear relationship? (1 point) Responses y=−5x+5 y equals negative 5 x plus 5 y=15x+5 y equals Start Fraction 1 over 5 End Fraction x plus 5 y=−x+5 y equals negative x plus 5 y=x+5 y equals x plus 5 Skip to navigation

Answer 1

To find the linear equation that represents the non-proportional linear relationship given the points in the table, we first need to establish the coordinates based on the values provided:

• (-5, 0)
• (0, 5)
• (2, 7)

Next, we can start by identifying the slope (m) of the line using two points. Let's use the points (0, 5) and (2, 7).

The formula for slope between two points (x1, y1) and (x2, y2) is:

\[ m = \frac{y2 - y1}{x2 - x1} \]

Substituting in our values:

\( m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \)

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

\[ y - y1 = m(x - x1) \]

Using the point (0, 5):

\[ y - 5 = 1(x - 0) \] \[ y - 5 = x \] \[ y = x + 5 \]

From the options given, the equation that matches our result is:

\[ y = x + 5 \]

Therefore, the answer to the question is:

y = x + 5