Final answer:
The equation in slope-intercept form representing the function shown in the table is: y = 3x + 1
Step-by-step explanation:
To write an equation in slope-intercept form representing the function shown in the table, we need to find the slope (m) and the y-intercept (b).
Given the points (-3, -8), (-1, -2), (1, 4), and (3, 10), we can find the slope using the formula:
m = (change in y)/(change in x)
Let's calculate the slope using two points from the table. Using (-3, -8) and (1, 4):
m = (4 - (-8))/(1 - (-3))
m = (4 + 8)/(1 + 3)
m = 12/4
m = 3
Now that we have the slope (m = 3), we can use the slope-intercept form of a linear equation, which is:
y = mx + b
Substituting the value of m, our equation becomes:
y = 3x + b
To find the value of the y-intercept (b), we can choose any point from the table and substitute its x and y values into the equation. Let's use the point (-1, -2):
-2 = 3(-1) + b
-2 = -3 + b
Simplifying the equation, we find:
b = -2 + 3
b = 1
Therefore, the equation in slope-intercept form representing the function shown in the table is: y = 3x + 1