Question

The points on the graph are (1,4) and (-3,8)
Determine the initial value and the rate of change of the liner function.

Answer 1

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

First, let's calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points (1,4) and (-3,8):

m = (8 - 4) / (-3 - 1)
m = 4 / -4
m = -1

Now that we have the slope, we can substitute it into the equation along with the coordinates of one of the points to calculate the y-intercept (b):

4 = -1(1) + b
4 = -1 + b
b = 4 + 1
b = 5

Therefore, the initial value (y-intercept) is 5 and the rate of change (slope) is -1.