Final answer:
The function rule for the line passing through the origin (0,0) and the point (-7,-16) is y = (16/7)x.
Step-by-step explanation:
The function rule for the line passing through the origin (0,0) and the point (-7,-16) can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
In this case, (x1, y1) = (0, 0) and (x2, y2) = (-7, -16)
So, m = (-16 - 0) / (-7 - 0) = -16 / -7 = 16/7
Step 2: Substitute the slope and the coordinates of one point (0,0) into the equation.
Using m = 16/7 and (x, y) = (0, 0), the equation becomes: y = (16/7)x + 0
Simplifying, the function rule is: y = (16/7)x