Question

Determine the initial value and the rate of change of the linear function as given in the graph. (1 point)

(-1.5,-3), (0,0), (0.5,1)

Answer 1

To determine the initial value and rate of change of the linear function, we can use the formula for the equation of a straight line:

y = mx + b

where m is the rate of change (slope) and b is the initial value (y-intercept).

Using the given points (-1.5,-3), (0,0), and (0.5,1), we can find the values of m and b.

1. Finding the slope (m):
To find the rate of change, we need to find the change in y divided by the change in x between any two points on the line.

From (-1.5,-3) to (0,0):
change in y = 0 - (-3) = 3
change in x = 0 - (-1.5) = 1.5

So the slope m = (change in y) / (change in x) = 3 / 1.5 = 2

2. Finding the initial value (b):
To find the initial value, we can substitute the x and y values of any point on the line into the equation.

Using the point (0,0):
0 = 2(0) + b
0 = b

So the initial value b = 0.

Therefore, the linear function can be written as y = 2x + 0, or simply y = 2x. The initial value is b = 0, and the rate of change is m = 2.