Question

HELP ASAPPPPP!!!

A graph of the exponential function f(x) is given.

The linear function f of x decreases through the ordered pairs negative 2,9 and negative 1,3 and 0,1 and 1,0.333

Write the equation to represent f(x).

Answer 1

To find the equation that represents the linear function f(x), we can use the given ordered pairs.

The ordered pairs given are:

(-2, 9)

(-1, 3)

(0, 1)

(1, 0.333)

To represent a linear function, we can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (change in y) / (change in x)

Let's calculate the slope using the first two points:

m = (3 - 9) / (-1 - (-2)) = -6 / 1 = -6

Now that we have the slope, we can substitute it into the slope-intercept form and use one of the points to find the y-intercept.

Using the point (-2, 9):

9 = -6(-2) + b

9 = 12 + b

b = 9 - 12

b = -3

Now we have the slope (m = -6) and the y-intercept (b = -3), so we can write the equation for the linear function f(x) as:

y = -6x - 3

This equation represents the linear function f(x) that decreases through the given ordered pairs.

Explanation: