Use the table to answer the question.
x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.
(1 point)
The rate of change is m=
, and the initial value is b=
.
To find the rate of change and the initial value of the linear function, we need to calculate the slope of the line using the given values.
The formula for calculating the slope (rate of change) is:
m = (change in y) / (change in x)
From the table, we can see that when x changes from 1 to -3, y changes from 4 to 8. The change in y is 8 - 4 = 4, and the change in x is -3 - 1 = -4.
So, the rate of change is m = 4 / -4 = -1.
This means that for every unit increase in x, y decreases by 1.
Next, we need to find the initial value (y-intercept). In the table, when x is 0, y is not given. However, we can calculate the y-intercept using the slope and a point from the table.
Let's use the point (1,4).
The equation of a line in slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Plugging in the values, we have:
4 = -1(1) + b
Rearranging the equation, we get:
4 = -1 + b
Adding 1 to both sides, we get:
5 = b
So, the initial value (y-intercept) b is 5.
Therefore, the rate of change (slope) is m = -1, and the initial value (y-intercept) b = 5.