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 we are given the point (-4, 4), we can find the slope of the line by selecting a second point on the line. From the graph, we can select the point (-2, 2) as our second point.
To find the slope, we use the formula: slope = (y2 - y1) / (x2 - x1)
Using the points (-4, 4) and (-2, 2), we find the slope as follows:
slope = (2 - 4) / (-2 - (-4))
= (-2) / (2)
= -1
So, we have found that the slope of the line is -1.
Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is any point on the line, and m is the slope.
Using the point (-4, 4) and the slope -1, we have:
y - 4 = -1(x - (-4))
y - 4 = -1(x + 4)
y - 4 = -x - 4
y = -x
Therefore, the equation of the function shown by the graph is y = -x.