Final answer:
The slope of the linear function f is -4/3, statement b is false, the zero of f is x = -2, and the x-intercept of f is false.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To find the slope, we use the formula: slope = (y2 - y1) / (x2 - x1). Using the given points (-4,0) and (2,-8), we can calculate the slope as follows:
slope = (-8 - 0) / (2 - (-4)) = (-8) / (2 + 4) = -8 / 6 = -4/3.
Since the slope of the linear function f is -4/3, statement a. The slope of the graph of f is -4, is false.
To determine if statement b. The graph of f passes through the point (1,-4) is true, we need to substitute the x and y values into the equation of the line. Using the equation y = mx + b, we can substitute the values (1,-4):
-4 = (-4/3)(1) + b
-4 = -4/3 + b
b = -4 + 4/3 = -12/3 + 4/3 = -8/3
So the y-intercept of the linear function f is -8/3, not -4. Therefore, statement b is false.
The zero of a function occurs when y = 0. To find the zero of f, we can set y = 0 in the equation y = mx + b and solve for x:
0 = (-4/3)x - 8/3
(4/3)x = -8/3
x = (-8/3) / (4/3) = -8/3 * 3/4 = -2
The zero of f is x = -2, not 4. So, statement c. The zero of f is 4 is false.
The x-intercept of a function occurs when y = 0. To find the x-intercept of f, we can set y = 0 and solve for x:
0 = (-4/3)x - 8/3
(4/3)x = -8/3
x = (-8/3) / (4/3) = -8/3 * 3/4 = -2
The x-intercept of f is x = -2, not -4. So, statement d. The x-intercept of the graph of f is -4 is false.