Question

The table shows a linear relationship between x and y. Find the rate of change of y with respect to x.

Answer 1

The rate of change of y with respect to x is
`(5)/(8)`.

How to determine the rate of change of a linear relationship

In accordace with statement, the table represents a linear relationship, that is, an equation of the form:

y = m · x + b

Where:

• x - Independent variable.
• y - Dependent variable.
• m - Slope, also known as rate of change.
• b - Intercept.

Rate of change is computed by secant line formula:

`m = (\Delta y)/(\Delta x)`

Finally, we proceed to determine the rate of change of the linear relationship:

`m = (4 - (- 11))/(16 - (- 8))`

`m = (15)/(24)`

`m = (5)/(8)`

Remark

There is a typing mistake in the table, - 5 must be written instead of - 8.5 in the y-row.