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Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Linear Function 1: y=x+8

Linear Function 2:

A coordinate plane shows the x-axis ranging from negative 2 to 6 in increments of 1 and the y-axis ranging from negative 2 to 12 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 2 comma 6 right parenthesis and left parenthesis 4 comma 10 right parenthesis. (1 point)
Linear Function
has the greater rate of change.

1 answer

To compare the rates of change of the two linear functions, we can analyze their slopes.

Linear Function 1: The equation is given as \( y = x + 8 \). The slope (rate of change) is the coefficient of \( x \), which is 1.

Linear Function 2: We need to calculate the slope using the two points provided: \( (2, 6) \) and \( (4, 10) \).

The formula for slope (m) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the values from the points:

  • \( (x_1, y_1) = (2, 6) \)
  • \( (x_2, y_2) = (4, 10) \)

Calculating the slope:

\[ m = \frac{10 - 6}{4 - 2} = \frac{4}{2} = 2 \]

Now we have the slopes:

  • Linear Function 1: slope = 1
  • Linear Function 2: slope = 2

Since 2 > 1, Linear Function 2 has the greater rate of change.

So the answer is: 2 for Linear Function 2.