Math Snap

STEP 1

1. A linear function is of the form $y = mx + b$, where $m$ and $b$ are constants, and $x$ is the variable.
2. A linear function graphically represents a straight line.
3. A function that is not linear will not fit the form $y = mx + b$.

STEP 2

1. Analyze each function to determine if it fits the linear form $y = mx + b$.
2. Identify which function does not fit this form.

STEP 3

Analyze function (a) $y = -\frac{2}{3}x + \frac{11}{2}$:
This function is in the form $y = mx + b$ where $m = -\frac{2}{3}$ and $b = \frac{11}{2}$. Therefore, it is a linear function.

STEP 4

Analyze function (b) $y = \frac{3 - 4x}{7}$:
This can be rewritten as:
$$y = \frac{3}{7} - \frac{4}{7}x$$ This is in the form $y = mx + b$ where $m = -\frac{4}{7}$ and $b = \frac{3}{7}$. Therefore, it is a linear function.

STEP 5

Analyze function (c) $y = \frac{7}{3 - 4x}$:
This function cannot be rewritten in the form $y = mx + b$ because it involves division by an expression containing $x$. This indicates a non-linear relationship.

STEP 6

Analyze function (d) $y = 3 - x$:
This function is in the form $y = mx + b$ where $m = -1$ and $b = 3$. Therefore, it is a linear function.

Identify which function is not linear:
From the analysis, function (c) $y = \frac{7}{3 - 4x}$ does not fit the form $y = mx + b$ and is therefore not a linear function.
The function that is not a linear function is $\boxed{c}$.