Question

Find the rate of change of the linear function from the point ​(0​,​12) to the point ​(​16,6​).

Answer 1

The answer is -3/8.

Explanation:

Hey there!

To find the rate of change, we can use the slope formula.

`\displaystyle m = (y_2 - y_1)/(x_2 - x_1)`

Our values for each are listed below:

• x₁ = 0
• x₂ = 16
• y₁ = 12
• y₂ = 6

Now, we need to do basic arithmetic to find the rate of change by substituting the known values for the coordinates into the slope formula.

`\displaystyle m = (6 - 12)/(16-0)`

Then, we can simplify by evaluating the numerator and the denominator separately:

`\displaystyle m = (-6)/(16)`

Finally, we can find the simplified version of this fraction:

`\displaystyle m = -(3)/(8)`

Therefore, the rate of change is -3/8.

Answer 2

-3/8

Explanation:

The rate of change is the same as the slope

m = ( y2-y1)/(x2-x1)

= ( 6-12)/(16-0)

= -6/16

= -3/8