Question

What is the function rule for the line?

Answer 1

(-3,0) and (0,-2)
slope = (-2 - 0)/(0 + 3) = -2/3
b = -2
so equation
y = -2/3(x) - 2

answer
B. f(x) = -2/3(x) - 2

Answer 2

Let's find the slope-intercept equation of this line.  You can read off the y-intercept immediately; it's the place where x= 0 and the line crosses the y-axis.  Here that intercept is b=-2.

The coordinates of that point are (0,-2).

Now let's find the slope of the line.  Starting at (0,-2) move to the left 3 units (because -3 is the x-coordinate of the intersection of the line with the x-axis).  From (0,-2), how far UP along the y-axis to the x-axis is it?

slope = rise / run.  In this case, starting from (0,-2), and moving 3 units to the left, we get "run" = -3.  Starting from (0,-2) and moving straight up to the x-axis, we get "rise" = 2.

The slope is then m = rise / run   =  2/-3, or    m = -2/3.

Thus, the equation of this line is y = mx + b, or   y = (-2/3)x - 2.