A slope is also known as the gradient of a line. The listed function that has a greater rate of change than the one in the graph is f(X)= x + 1.
A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The coordinates through which the line of the graph is passing are (0,-4) and (6,0). Thus, the slope of the given line is,
Slope, m = (-4 - 0)/(0 - 6) = -4/-6 = 2/3 = 0.6667
Comparing the given equation with the general equation of a line, y=mx+c, where m is the slope of the line. Therefore, the slope of the given lines is,
A. f(X)= -0.3x + 2
slope = -0.3x
Hence, the slope is less than the slope of the given graph.
B. f(X)= x + 1
slope = 1
Hence, the slope is greater than the slope of the given graph.
C. f(X)= 0.1x + 2
slope = 0.1x
Hence, the slope is less than the slope of the given graph.
D. f(X)= -0.25x - 3
slope = -0.25x
Hence, the slope is less than the slope of the given graph.
Hence, the listed function that has a greater rate of change than the one in the graph is f(X)= x + 1.
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