The function rule for the graph, given the slope and the points on the graph would be y = (-1/4)x - 1
How to find the function rule ?
To write a function rule for the given graph with two points (0, -1) and (4, -2), you can use the slope-intercept form of a linear equation, which is:
y = mx + b
Calculate the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (0, -1) and (x2, y2) = (4, -2):
m = (-2 - (-1)) / (4 - 0)
m = (-2 + 1) / 4
m = -1/4
Use one of the points to find the y-intercept (b):
y = mx + b
-1 = (-1/4)(0) + b
-1 = 0 + b
b = -1
The function rule for the graph:
y = (-1/4)x - 1