Question

A linear function can be used to model the relationship between x and y that is shown in the table below:

x: 3 5 7 9
y: -2 4 10 16
What is the equation of this linear function?
A) y=3x+3
B) y=3x−11
C) y=6x−2
D) y=6x−20

Answer 1

The equation of the linear function is y = 3x - 11.

Step-by-step explanation:

The equation of the linear function can be found by determining the slope (m) and y-intercept (b) from the given table of values. The slope can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Taking any two points from the table, let's say (3, -2) and (5, 4), substituting the values into the formula:
m = (4 - (-2)) / (5 - 3)
m = 6 / 2
m = 3

The y-intercept (b) can be determined by substituting the slope (m) and any point from the table into the equation:
y = mx + b
Let's use the point (3, -2):
-2 = 3(3) + b
-2 = 9 + b
b = -11

Therefore, the equation of the linear function is:
y = 3x - 11