Question

a. $y = -\frac{3}{4}x$ b. $y = \frac{1}{2}$ c. $y = -3 + 2x$ d. $y = 3x^2 - 2$
notes:
pour écrire léquation dune fonction linéaire, nous devons connaître le taux de variation, ou le coefficient directeur. une ______, ces valeurs obtenues, nous pouvons écrire les équations des fonctions linéaires avec lordonnée à lorigine, ou $b = 0$. ______,
review
si vous connaissez la pente et les coordonnées dune relation linéaire, suivez les étapes ci-dessous.
équations à partir dun point et dune pente
pente = 3

• nommez $x$ et $y$ dans léquation ______ ______.
• remplacez toutes les valeurs dans léquation: ________.
• résolvez léquation pour ________.
• écrivez léquation sous la forme pente-ordonnée à lorigine

Explanation:

To determine which function is linear, we recall the definition of a linear function: a linear function has the form \( y = mx + b \), where \( m \) (slope) and \( b \) (y - intercept) are constants, and the highest power of \( x \) is 1.

Analyze Option A: \( y = -\frac{3}{4}x \)

This function can be written as \( y=-\frac{3}{4}x + 0 \), where \( m=-\frac{3}{4} \) and \( b = 0 \). The power of \( x \) is 1, so it is a linear function.

Analyze Option B: \( y=\frac{3}{2} \)

This function can be written as \( y = 0x+\frac{3}{2} \), where \( m = 0 \) and \( b=\frac{3}{2} \). The power of \( x \) is 0 (since \( x^0 = 1\) when \( x
eq0\)), and it is also a linear function (a horizontal line).

Analyze Option C: \( y=- 3 + 2x \)

We can rewrite it as \( y=2x-3 \), where \( m = 2 \) and \( b=-3 \). The power of \( x \) is 1, so it is a linear function.

Analyze Option D: \( y = 3x^{2}-2 \)

In this function, the highest power of \( x \) is 2. A function with \( x \) raised to the power of 2 is a quadratic function (a parabola), not a linear function.

If we assume the question is to find the non - linear function, the answer is D. \( y = 3x^{2}-2 \)

If we assume the question is to find linear functions, the linear functions are:
A. \( y = -\frac{3}{4}x \)
B. \( y=\frac{3}{2} \)
C. \( y=-3 + 2x \)

Since the original problem is not fully clear (it seems to be a multiple - choice question about identifying linear/non - linear functions), if we consider the most probable case where we need to find the non - linear one:

Answer:

D. \( y = 3x^{2}-2 \)