QuestionA linear equation is given. $y=8-\frac{x}{5}$
This $\square$ a proportional relationship because

Studdy Solution

STEP 1

1. A proportional relationship is one where two quantities vary directly with each other, often expressed as $y = kx$ , where $k$ is a constant.
2. In a proportional relationship, the graph is a straight line through the origin.

STEP 2

1. Identify the form of the given equation.
2. Compare the equation to the form of a proportional relationship.
3. Determine if the equation represents a proportional relationship.

STEP 3

Identify the form of the given equation:
The given equation is:
$y = 8 - \frac{x}{5}$
This is a linear equation in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 4

Compare the equation to the form of a proportional relationship:
A proportional relationship has the form $y = kx$ , which implies:
1. The line passes through the origin $(0,0)$ .
2. There is no constant term added or subtracted.
In the given equation $y = 8 - \frac{x}{5}$ , there is a constant term $8$ .

STEP 5

Determine if the equation represents a proportional relationship:
Since the equation $y = 8 - \frac{x}{5}$ has a constant term $8$ , it does not pass through the origin. Therefore, it is not in the form $y = kx$ .
Thus, this equation does not represent a proportional relationship.
The equation $y = 8 - \frac{x}{5}$ is not a proportional relationship because it includes a constant term and does not pass through the origin.

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