Question What does $k$ represent in $\mathbf{y}=\mathbf{k x}$ ? Constant of proportionality.

Studdy Solution

STEP 1

Assumptions
1. The equation given is $\mathbf{y} = \mathbf{kx}$ .
2. We are to determine the role of $k$ in this equation.

STEP 2

Understand the structure of the equation.
The equation $\mathbf{y} = \mathbf{kx}$ is a linear equation in two variables, $x$ and $y$ .

STEP 3

Identify the components of the linear equation.
In a linear equation of the form $y = mx + b$ :
- $y$ is the dependent variable. - $x$ is the independent variable. - $m$ is the slope or the constant of proportionality. - $b$ is the y-intercept.

STEP 4

Compare the given equation with the standard form.
The given equation $\mathbf{y} = \mathbf{kx}$ does not have a $b$ term, which means the y-intercept is $0$ .

STEP 5

Determine the role of $k$ .
Since $k$ is the coefficient of $x$ and there is no y-intercept term, $k$ represents the slope or the constant of proportionality in the equation $\mathbf{y} = \mathbf{kx}$ .
$k$ does not represent the y-intercept, dependent variable, or independent variable.
The solution is that $k$ represents the constant of proportionality.

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