What is the equation of the function shown by the graph? Show your work. Remember to find two integer points where the line passes through so you can calculate the slope. (Hint: One is (-4, 4) Find the second point)
Since the graph of the function passes through (-4, 4), we can use this point to calculate the slope of the line.
Let's find a second point on the line by visually determining another integer point. By looking at the graph, we can see that the point (-1, 3) also lies on the line.
Now we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the coordinates (-4, 4) and (-1, 3) will be used:
m = (3 - 4) / (-1 - (-4))
m = (-1) / (3)
m = -1/3
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the function. Let's choose the point (-4, 4) to write the equation:
y - y1 = m(x - x1)
(y - 4) = (-1/3)(x - (-4))
(y - 4) = (-1/3)(x + 4)
Expanding the equation:
y - 4 = (-1/3)x - (4/3)
Finally, rearranging the equation to slope-intercept form:
y = (-1/3)x - (4/3) + 4
y = (-1/3)x - (4/3) + (12/3)
y = (-1/3)x + 8/3
So, the equation of the function shown by the graph is y = (-1/3)x + 8/3.