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.
(-4, 4)
(4,-1)
To find the equation of the function, we first need to find the slope of the line. The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. Using the points (-4, 4) and (4, -1), we can calculate the slope:
m = (-1 - 4) / (4 - (-4))
m = (-5) / 8
m = -5/8
Now that we have the slope, 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)
Using the point (-4, 4) and the slope -5/8, we can substitute these values into the equation:
y - 4 = (-5/8)(x - (-4))
Simplifying:
y - 4 = (-5/8)(x + 4)
y - 4 = (-5/8)x - 5/2
y = (-5/8)x - 5/2 + 4
y = (-5/8)x - 5/2 + 8/2
y = (-5/8)x + 3/2
Thus, the equation of the function shown by the graph is y = (-5/8)x + 3/2.