The table represents some points on the graph of a linear function. Write a function that represents this relationship.
x -4, -2, 6 y 10, 7, -5
To find the equation of the line passing through the points (-4, 10), (-2, 7), and (6, -5), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (-4, 10) and (x2, y2) = (-2, 7).
m = (7 - 10) / (-2 - (-4)) = -3 / 2 = -1.5
Next, we can use one of the points to find the y-intercept. For example, using the point (-4, 10):
10 = -1.5(-4) + b
10 = 6 + b
b = 4
Therefore, the function representing this relationship is y = -1.5x + 4.