Answer:
To find the equation of the linear function represented by the given table, we need to determine the slope and y-intercept. The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.
To calculate the slope (m), we can use any two points from the table. Let's choose the points (-1, 0) and (1, -4). The formula for calculating slope is:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the chosen points:
m = (-4 - 0) / (1 - (-1))
m = -4 / 2
m = -2
Now that we have the slope, we can proceed to find the y-intercept (b). We can choose any point from the table and substitute its coordinates into the slope-intercept form equation. Let's use the point (1, -4):
-4 = (-2)(1) + b
-4 = -2 + b
b = -4 + 2
b = -2
Therefore, the equation of the linear function represented by the given table in slope-intercept form is:
y = -2x - 2
In this equation, the coefficient of x (-2) represents the slope, while the constant term (-2) represents the y-intercept.
Explanation: