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