To determine the initial value and the rate of change of the linear function, we can use the formula for the equation of a line:
y = mx + b
where m is the rate of change (slope) and b is the initial value (y-intercept).
Let's use the points (0,3) and (3,2) to find the rate of change.
First, we find the change in y:
Δy = 2 - 3 = -1
Next, we find the change in x:
Δx = 3 - 0 = 3
Now we can find the rate of change (slope) using the formula:
m = Δy / Δx = -1 / 3 ≈ -0.333 (rounded to three decimal places)
Now let's find the initial value (y-intercept) by substituting the slope and one of the points into the equation:
y = mx + b
3 = (-0.333)(0) + b
3 = b
Therefore, the initial value is 3, and the rate of change is approximately -0.333.
Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.
There are 4 points on the graph, (-3, 4), (0, 3), (3, 2), (6, 1).
The initial value is ___, and the rate of change is ___.
3 answers
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Apologies for the previous incorrect response. Let's reevaluate the problem.
To determine the initial value and the rate of change of the linear function, we can use the formula for the equation of a line:
y = mx + b
where m is the rate of change (slope) and b is the initial value (y-intercept).
Let's use the points (-3, 4) and (6, 1) to find the rate of change.
First, we find the change in y:
Δy = 1 - 4 = -3
Next, we find the change in x:
Δx = 6 - (-3) = 9
Now we can find the rate of change (slope) using the formula:
m = Δy / Δx = -3 / 9 = -0.333 (rounded to three decimal places)
The rate of change is -0.333.
To find the initial value (y-intercept), we can choose any point on the line. Let's use the point (-3, 4) and substitute the values into the equation:
4 = (-0.333)(-3) + b
4 = 0.999 + b
b = 4 - 0.999
b = 3.001 (rounded to three decimal places)
The initial value is 3.001.
Therefore, the initial value is 3.001, and the rate of change is approximately -0.333.
To determine the initial value and the rate of change of the linear function, we can use the formula for the equation of a line:
y = mx + b
where m is the rate of change (slope) and b is the initial value (y-intercept).
Let's use the points (-3, 4) and (6, 1) to find the rate of change.
First, we find the change in y:
Δy = 1 - 4 = -3
Next, we find the change in x:
Δx = 6 - (-3) = 9
Now we can find the rate of change (slope) using the formula:
m = Δy / Δx = -3 / 9 = -0.333 (rounded to three decimal places)
The rate of change is -0.333.
To find the initial value (y-intercept), we can choose any point on the line. Let's use the point (-3, 4) and substitute the values into the equation:
4 = (-0.333)(-3) + b
4 = 0.999 + b
b = 4 - 0.999
b = 3.001 (rounded to three decimal places)
The initial value is 3.001.
Therefore, the initial value is 3.001, and the rate of change is approximately -0.333.