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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

The Table Shows A Linear Relationship Between X And Y What Is The Rate Of Change Of Y With Respect To X A 92 B 29 C 29 D 92 class=

Sagot :

akposevictor

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

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:

[tex]\frac{\triangle y}{\triangle x} =\frac{y_2-y_1}{x_2-x_1} \\[/tex]

From the table:

[tex]x_1=-20, x_2=-12, y_1=96, y_2=60[/tex]

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

[tex]\frac{\triangle y}{\triangle x} =\frac{60-96}{-12-(-20)} \\\\\frac{\triangle y}{\triangle x} =\frac{-36}{8}[/tex]

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

[tex]\frac{\triangle y}{\triangle x} =\frac{-9}{2}[/tex]

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

Learn more on rate of change here: https://brainly.com/question/8728504

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