Question

2.2.2 evaluation & function types
pregunta 1 de 7 (1 punto) intento de respuesta 1 de limitados

ecuación	¿es la ecuación lineal?
(b) ( y = -4x + 1 )	no, sí (seleccionado)
(c) ( y = 4x^2 + 8 )	no, sí (seleccionado)
(d) ( y = -6 )	sí (seleccionado), no

Explanation:

To determine if an equation is linear, we recall that a linear equation in two variables has the form \( y = mx + b \), where \( m \) and \( b \) are constants and the highest power of \( x \) is 1. Let's analyze each equation:

(a) \( y = x \)

• This can be written as \( y = 1x + 0 \), where \( m = 1 \) and \( b = 0 \). The highest power of \( x \) is 1, so it is linear. The selected "Sí" (Yes) is correct.

(b) \( y = -4x + 1 \)

• This is in the form \( y = mx + b \) with \( m = -4 \) and \( b = 1 \). The highest power of \( x \) is 1, so it is linear. The selected "No" is incorrect; it should be "Sí".

(c) \( y = 4x^2 + 8 \)

• The highest power of \( x \) is 2 (from \( x^2 \)), so it is a quadratic (non - linear) equation. The selected "No" is correct.

(d) \( y = -6 \)

• This can be written as \( y = 0x - 6 \), where \( m = 0 \) and \( b = -6 \). The highest power of \( x \) is 1, so it is linear (a horizontal line). The selected "Sí" is correct.

For part (b), the correct answer should be "Sí" (select the "Sí" radio button). For the other parts: (a) is correct as "Sí", (c) is correct as "No", (d) is correct as "Sí".

Answer:

To determine if an equation is linear, we recall that a linear equation in two variables has the form \( y = mx + b \), where \( m \) and \( b \) are constants and the highest power of \( x \) is 1. Let's analyze each equation:

(a) \( y = x \)

• This can be written as \( y = 1x + 0 \), where \( m = 1 \) and \( b = 0 \). The highest power of \( x \) is 1, so it is linear. The selected "Sí" (Yes) is correct.

(b) \( y = -4x + 1 \)

• This is in the form \( y = mx + b \) with \( m = -4 \) and \( b = 1 \). The highest power of \( x \) is 1, so it is linear. The selected "No" is incorrect; it should be "Sí".

(c) \( y = 4x^2 + 8 \)

• The highest power of \( x \) is 2 (from \( x^2 \)), so it is a quadratic (non - linear) equation. The selected "No" is correct.

(d) \( y = -6 \)

• This can be written as \( y = 0x - 6 \), where \( m = 0 \) and \( b = -6 \). The highest power of \( x \) is 1, so it is linear (a horizontal line). The selected "Sí" is correct.

For part (b), the correct answer should be "Sí" (select the "Sí" radio button). For the other parts: (a) is correct as "Sí", (c) is correct as "No", (d) is correct as "Sí".