Final answer:
The slope-intercept equation for the linear function represented by the table is y = (3/2)x - 4.
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the equation for the linear function represented by the table, we need to first find the slope and the y-intercept.
To find the slope, we can choose any two points from the table and use the formula:
m = (y2 - y1) / (x2 - x1).
Let's choose the points (2, -1) and (4, 2). Plugging these values into the formula, we get :
m = (2 - (-1)) / (4 - 2) = 3/2.
Now, let's find the y-intercept. We can choose any point from the table and use the formula:
b = y - mx.
Let's choose the point (2, -1). Plugging these values into the formula, we get"
b = -1 - (3/2)(2)
= -4.
Therefore, the slope-intercept equation for the linear function represented by the table is y = (3/2)x - 4.