Answer:
y = (5/2)x + 13/2
y = 3
y = -2x + 6
Step-by-step explanation:
The left part of the function which is a line sloping up to the right contains points (-3, -1) and (-1, 4) which can be read off the graph.
Since we have two points, we can find the equation.
You can use the slope formula given two points, but I will read it off the graph with rise and run.
Go from point (-3, -1) to point (-1, 4) by going up 5 (the rise) and going right 2 (the run).
slope = rise/run = 5/2
y = mx + b
y = (5/2)x + b
Use point (-1, 4) for x and y and solve for b.
4 = (5/2)(-1) + b
8/2 + 5/2 = b
b = 13/2
y = (5/2)x + 13/2
This is the first answer.
The middle part is a horizontal line in which every point has y-coordinate 3.
The equation is:
y = 3
This is the second answer.
The right part is the line that slopes down to the right. We can read two points easily. Use points (3, 0) and (2, 2).
Start at (3, 0). Go left 1 (run of -1) and up 2 (rise of 2). Now you are at point (2, 2).
slope = rise/run = 2/(-1) = -2
Now we find the y-intercept on the graph. After you get to (2, 2), keep moving with the same run and rise of the slope. Go left 1 and up 2 to point (1, 4). Go again left 1 and up 2 to (0, 6). Point (0, 6) is on the y-axis, so it is the y-intercept.
b = 6
y = mx + b
y = -2x + 6
This is the third answer.
