To find the equation of the linear function represented by the table in slope-intercept form (y = mx + b), you need to determine the slope (m) and the y-intercept (b) based on the given data points.
Given points from the table:
(1, 8)
(2, 12)
(3, 16)
(4, 20)
Step 1: Calculate the slope (m) using two of the points. You can choose any two points, such as (1, 8) and (4, 20):
m = (y2 - y1) / (x2 - x1)
m = (20 - 8) / (4 - 1)
m = 12 / 3
m = 4
Step 2: Now that you have the slope (m), you can use it to find the y-intercept (b) by substituting the values of one of the points into the equation. Let's use (1, 8):
8 = 4(1) + b
Now, solve for b:
8 = 4 + b
Subtract 4 from both sides:
b = 8 - 4
b = 4
So, the slope (m) is 4, and the y-intercept (b) is 4. Now, you can write the equation of the linear function in slope-intercept form:
y = 4x + 4