Question
(-4, -10/3) (-1, -4/3
Determine the initial value, and the rate of change of the linear function has given in the graph
A) the initial value is 2/3 and the rate of change is -2/3
B) the initial value is 1/6 and the rate of change is 3/2
C) the initial value is -2/3 and the rate of change is 2/3
D) the initial value is -2 and the rate of change is 2/3
Determine the initial value, and the rate of change of the linear function has given in the graph
A) the initial value is 2/3 and the rate of change is -2/3
B) the initial value is 1/6 and the rate of change is 3/2
C) the initial value is -2/3 and the rate of change is 2/3
D) the initial value is -2 and the rate of change is 2/3
Answers
GPT 3.5
To determine the initial value and rate of change of the linear function from the given points (-4, -10/3) and (-1, -4/3), we can use the formula for the slope of a line which is (y2 - y1) / (x2 - x1) and then substitute one of the points into the equation of the line to solve for the initial value.
Slope = (-4/3 - (-10/3)) / (-1 - (-4))
Slope = (6/3) / 3
Slope = 2/3
Now, let's use the point (-1, -4/3) to find the initial value (intercept) of the line:
y = mx + b
-4/3 = (2/3)(-1) + b
-4/3 = -2/3 + b
b = -4/3 + 2/3
b = -2/3
So, the initial value is -2/3 and the rate of change (slope) is 2/3. Therefore, the correct answer is:
C) the initial value is -2/3 and the rate of change is 2/3
Slope = (-4/3 - (-10/3)) / (-1 - (-4))
Slope = (6/3) / 3
Slope = 2/3
Now, let's use the point (-1, -4/3) to find the initial value (intercept) of the line:
y = mx + b
-4/3 = (2/3)(-1) + b
-4/3 = -2/3 + b
b = -4/3 + 2/3
b = -2/3
So, the initial value is -2/3 and the rate of change (slope) is 2/3. Therefore, the correct answer is:
C) the initial value is -2/3 and the rate of change is 2/3