Question

. The formula 9x - 5y = -160 relates the

temperature in degrees Fahrenheit y to
the temperature in degrees Celsius x.
Tell whether the relationship is a direct
variation. Explain your answer.

Answer 1

Answer: formula 9x - 5y = -160 is not a direct variation.

Step-by-step explanation: The provided expression, 9x - 5y = -160, does not exemplify direct variation.

Direct variation is a correlation existing between two variables, wherein one is a constant scalar multiple of the other. Stated differently, should one variable increase by a defined magnitude, the corresponding variable will also experience a commensurate increase of identical magnitude.

The formula provided indicates the absence of a constant proportionality between the temperature in degrees Celsius (x) and the temperature in degrees Fahrenheit (y). It is noteworthy that the correlation amidst the variables x and y is non-linear in nature, thereby precluding its representation in the form of a direct proportionality.

Answer 2

Answer: It is not a direct variation.

Explanation:

While a linear equation is a direct variation, the y-intercept of a direct variation relationship must be 0. Here, that is not the case. Let us manipulate this equation into a slope-intercept equation.

Given:

9x - 5y = -160

Add 5y and 160 to both sides of the equation:

5y = 9x + 160

Divide both sides of the equation by 5:

y =
`(9)/(5)`x + 32

32 ≠ 0