Question

Выберите функции, графики которых параллельны, ответ обоснуйте: A) у=6 и у=х+6B) у=х+3 и у=2х+3C) у=-4х-4 и у=-8х-8D) у=-3х+5 и у=-3х+6E) у=0,5х+3 и у=2х+3

Answer 1

A) у=6 и у=х+6

The functions у=6 and у=х+6 are parallel because they have the same slope. In both cases, the coefficient of х is 1, which means that the slope of the line is 1. Since the slopes are equal, the lines are parallel.

B) у=х+3 и у=2х+3

The functions у=х+3 and у=2х+3 are parallel because they have the same slope. In both cases, the coefficient of х is 1, which means that the slope of the line is 1. Since the slopes are equal, the lines are parallel.

C) у=-4х-4 и у=-8х-8

The functions у=-4х-4 and у=-8х-8 are parallel because they have the same slope. In both cases, the coefficient of х is -4, which means that the slope of the line is -4. Since the slopes are equal, the lines are parallel.

D) у=-3х+5 и у=-3х+6

The functions у=-3х+5 and у=-3х+6 are not parallel because they have different slopes. In the first equation, the coefficient of х is -3, which means that the slope of the line is -3. In the second equation, the coefficient of х is also -3, which means that the slope of the line is also -3. Since the slopes are different, the lines are not parallel.

E) у=0.5х+3 и у=2х+3

The functions у=0.5х+3 and у=2х+3 are not parallel because they have different slopes. In the first equation, the coefficient of х is 0.5, which means that the slope of the line is 0.5. In the second equation, the coefficient of х is 2, which means that the slope of the line is 2. Since the slopes are different, the lines are not parallel.

In summary, the functions A) у=6 and у=х+6, and B) у=х+3 and у=2х+3 are parallel because they have the same slopes. However, the functions C) у=-4х-4 and у=-8х-8, D) у=-3х+5 and у=-3х+6, and E) у=0.5х+3 and у=2х+3 are not parallel because they have different slopes