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Functions Unit Test

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Question
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 (slopes) of the two linear functions, we first need to determine the slope of each function.

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

Linear Function 2:
We have two points on the line: \( (2, 6) \) and \( (4, 10) \). To find the slope between these two points, we use the formula:

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

Substituting the coordinates:

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

Now, we can compare the rates of change:

  • Rate of change for Linear Function 1: \( 1 \)
  • Rate of change for Linear Function 2: \( 2 \)

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

Therefore, the answer is:

2 for Linear Function 2 has the greater rate of change.