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.
To determine which linear function has the greater rate of change, we need to compare the slopes of the two functions.
The slope-intercept form of a linear function is y = mx + b, where m is the slope of the line.
For Linear Function 1: y = x + 8, the slope (m) is 1.
For Linear Function 2, we can find the slope by using the coordinates of the plotted points. The slope (m) is calculated by (change in y)/(change in x). We have (4, 10) and (2, 6), so the change in y is 10 - 6 = 4, and the change in x is 4 - 2 = 2. Therefore, the slope is (4/2) = 2.
Since the slope of Linear Function 2 is greater than the slope of Linear Function 1, we can conclude that Linear Function 2 has the greater rate of change.
Therefore, the answer is: Linear Function 2 has the greater rate of change.