The slope of the function, f(x) can be determined by choosing two sets of ordered pairs from the table and substituting their values into the slope formula.
Let (x1, y1) = (0, -1)
(x2, y2) = (1, 7)
Plug these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [7 - (-1)] / [1 - 0]
m = (7 + 1) / 1
m = 8/1 or 8.
Therefore, the slope of f(x), m = 8.
The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.
The equation of the linear function, f(x) is:
f(x) = 8x - 1.
Given the slope-intercept form, y = mx + b, where m represents the slope of the line, and b represents the y-intercept:
The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.
Comparing the slope and y-intercept of the two functions, f(x) and g(x):
The slope of f(x), m = 8 is greater and steeper than the slope of g(x), m = 3. The y-intercept of f(x), b = -1 is greater than the y-intercept of g(x), b = -2.
Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.
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