Question

The table shows a linear relationship between x and y. What is the rate of change of y with respect to x.
A. -9/2
B. 2/9
C. -2/9
D. 9/2

Answer 1

Answer:

A. -⁹/2

Step-by-step explanation:

Using any two pairs of values form the table, say (-12, 60) and (-6, 33),

Rate of change = ∆y/∆x

= (33 - 60) / (-6 -(-12))

= -27/6

= -9/2

Rate of change = -⁹/2

Answer 2

The rate of change of y with respect to x is -9/2

Option A is correct

For a linear relationship, the rate of change of y with respect to x is given by the formula:

$\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1}$

From the table:

$x_1=-20, x_2=-12, y_1=96, y_2=60$

Substitute $x_1=-20, x_2=-12, y_1=96, y_2=60$ into the equation $\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1}$

$\frac{\triangle y}{\triangle x} =\frac{60-96}{-12-(-20)} \\\\\frac{\triangle y}{\triangle x} =\frac{-36}{8}$

Reduce the expression to the lowest term by dividing the numerator and denominator by 4

$\frac{\triangle y}{\triangle x} =\frac{-9}{2}$

The rate of change of y with respect to x is -9/2

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