The question is asking for the equation of each of the line segments.
The first equation is -6 ≤ x ≤ -2. The coordinates are (-6, 2) and (-2, -2)
Find the slope by counting the [tex] \frac{rise}{run} [/tex] = [tex] \frac{-4}{4} [/tex] = -1.
Now plug in the slope and ONE of the coordinates into the point-slope equation and solve for y: y - y₁ = m(x - x₁); where (x₁, y₁) is the chosen point.
I am choosing to use (-6, 2):
y - 2 = -1(x - (-6))
y - 2 = -(x +6)
y - 2 = -x -6
y = -x - 4
Notice that "f(x) =" is already on the left side of your worksheet, so you only need to write "-x - 4" on the first line.
Try this procedure for the second and third lines and check your answers below: Hints: slope for 2nd line is 0, slope for 3rd line is [tex] \frac{1}{2} [/tex]
2nd line: -3
3rd line: [tex] \frac{1}{2} [/tex]x - [tex] \frac{7}{2} [/tex] This can also be written as [tex] \frac{x-7}{2} [/tex]
Answers:
-x - 4
-3
[tex] \frac{x-7}{2} [/tex]
